diff --git a/mindspore/nn/probability/distribution/__init__.py b/mindspore/nn/probability/distribution/__init__.py
index 2f83d36ab0a..db8dad5c3cf 100644
--- a/mindspore/nn/probability/distribution/__init__.py
+++ b/mindspore/nn/probability/distribution/__init__.py
@@ -24,6 +24,7 @@ from .exponential import Exponential
 from .uniform import Uniform
 from .geometric import Geometric
 from .categorical import Categorical
+from .log_normal import LogNormal
 
 __all__ = ['Distribution',
            'TransformedDistribution',
@@ -32,4 +33,6 @@ __all__ = ['Distribution',
            'Exponential',
            'Uniform',
            'Categorical',
-           'Geometric',]
+           'Geometric',
+           'LogNormal',
+           ]
diff --git a/mindspore/nn/probability/distribution/distribution.py b/mindspore/nn/probability/distribution/distribution.py
index 87a963ea6d3..ca6cabea436 100644
--- a/mindspore/nn/probability/distribution/distribution.py
+++ b/mindspore/nn/probability/distribution/distribution.py
@@ -76,7 +76,10 @@ class Distribution(Cell):
                 self._parameters[k] = param[k]
 
         # some attributes
-        self.parameter_type = set_param_type(self.parameters['param_dict'], dtype)
+        if 'distribution' in self.parameters.keys():
+            self.parameter_type = self.parameters['distribution'].parameter_type
+        else:
+            self.parameter_type = set_param_type(self.parameters['param_dict'], dtype)
         self._broadcast_shape = self._calc_broadcast_shape()
         self._is_scalar_batch = self._check_is_scalar_batch()
 
@@ -206,8 +209,8 @@ class Distribution(Cell):
         """
         Check if the parameters used during initialization are scalars.
         """
-        if hasattr(self, 'distribution'):
-            return self._distribution.is_scalar_batch
+        if 'distribution' in self.parameters.keys():
+            return self.parameters['distribution'].is_scalar_batch
         param_dict = self.parameters['param_dict']
         for value in param_dict.values():
             if value is None:
@@ -220,8 +223,8 @@ class Distribution(Cell):
         """
         Calculate the broadcast shape of the parameters used during initialization.
         """
-        if hasattr(self, 'distribution'):
-            return self._distribution.broadcast_shape
+        if 'distribution' in self.parameters.keys():
+            return self.parameters['distribution'].broadcast_shape
         param_dict = self.parameters['param_dict']
         broadcast_shape_tensor = None
         for value in param_dict.values():
diff --git a/mindspore/nn/probability/distribution/log_normal.py b/mindspore/nn/probability/distribution/log_normal.py
new file mode 100644
index 00000000000..f3d1eebc7ba
--- /dev/null
+++ b/mindspore/nn/probability/distribution/log_normal.py
@@ -0,0 +1,235 @@
+# Copyright 2020 Huawei Technologies Co., Ltd
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ============================================================================
+"""LogNormal Distribution"""
+import numpy as np
+from mindspore.ops import operations as P
+from mindspore.common import dtype as mstype
+import mindspore.nn.probability.bijector as msb
+import mindspore.nn.probability.distribution as msd
+from ._utils.utils import check_distribution_name
+from ._utils.custom_ops import exp_generic, expm1_generic, log_generic
+
+class LogNormal(msd.TransformedDistribution):
+    """
+    LogNormal distribution.
+    A log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose
+    logarithm is normally distributed. It is constructed as the exponential transformation of a Normal distribution.
+
+    Args:
+        loc (int, float, list, numpy.ndarray, Tensor, Parameter): The mean of the underlying Normal distribution.
+        scale (int, float, list, numpy.ndarray, Tensor, Parameter): The standard deviation of the underlying
+          Normal distribution.
+        seed (int): the seed used in sampling. The global seed is used if it is None. Default: None.
+        dtype (mindspore.dtype): type of the distribution. Default: mstype.float32.
+        name (str): the name of the distribution. Default: 'LogNormal'.
+
+    Note:
+        `scale` must be greater than zero.
+        `dist_spec_args` are `loc` and `scale`.
+        `dtype` must be a float type because LogNormal distributions are continuous.
+
+    Examples:
+        >>> # To initialize a LogNormal distribution of `loc` 3.0 and `scale` 4.0.
+        >>> n = msd.LogNormal(3.0, 4.0, dtype=mstype.float32)
+        >>>
+        >>> # The following creates two independent LogNormal distributions.
+        >>> n = msd.LogNormal([3.0, 3.0], [4.0, 4.0], dtype=mstype.float32)
+        >>>
+        >>> # A LogNormal distribution can be initilize without arguments.
+        >>> # In this case, `loc` and `scale` must be passed in during function calls.
+        >>> n = msd.LogNormal(dtype=mstype.float32)
+        >>>
+        >>> # To use a LogNormal distribution in a network.
+        >>> class net(Cell):
+        >>>     def __init__(self):
+        >>>         super(net, self).__init__():
+        >>>         self.n1 = msd.LogNormal(0.0, 1.0, dtype=mstype.float32)
+        >>>         self.n2 = msd.LogNormal(dtype=mstype.float32)
+        >>>
+        >>>     # The following calls are valid in construct.
+        >>>     def construct(self, value, loc_b, scale_b, loc_a, scale_a):
+        >>>
+        >>>         # Private interfaces of probability functions corresponding to public interfaces, including
+        >>>         # `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`, have the same
+        >>>         # arguments as follows.
+        >>>         # Args:
+        >>>         #     value (Tensor): the value to be evaluated.
+        >>>         #     loc (Tensor): the loc of distribution. Default: None. If `loc` is passed in as None,
+        >>>         #         the mean of the underlying Normal distribution will be used.
+        >>>         #     scale (Tensor): the scale of distribution. Default: None. If `scale` is passed in as None,
+        >>>         #         the standard deviation of the underlying Normal distribution will be used.
+        >>>
+        >>>         # Examples of `prob`.
+        >>>         # Similar calls can be made to other probability functions
+        >>>         # by replacing 'prob' by the name of the function.
+        >>>         ans = self.n1.prob(value)
+        >>>         # Evaluate with respect to distribution b.
+        >>>         ans = self.n1.prob(value, loc_b, scale_b)
+        >>>         # `loc` and `scale` must be passed in during function calls since they were not passed in construct.
+        >>>         ans = self.n2.prob(value, loc_a, scale_a)
+        >>>
+        >>>
+        >>>         # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments.
+        >>>         # Args:
+        >>>         #     loc (Tensor): the loc of distribution. Default: None. If `loc` is passed in as None,
+        >>>         #         the mean of the underlying Normal distribution will be used.
+        >>>         #     scale (Tensor): the scale of distribution. Default: None. If `scale` is passed in as None,
+        >>>         #         the standard deviation of the underlying Normal distribution will be used.
+        >>>
+        >>>         # Example of `mean`. `sd`, `var`, and `entropy` are similar.
+        >>>         ans = self.n1.mean() # return 0.0
+        >>>         ans = self.n1.mean(loc_b, scale_b) # return mean_b
+        >>>         # `loc` and `scale` must be passed in during function calls since they were not passed in construct.
+        >>>         ans = self.n2.mean(loc_a, scale_a)
+        >>>
+        >>>
+        >>>         # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
+        >>>         # Args:
+        >>>         #     dist (str): the type of the distributions. Only "Normal" is supported.
+        >>>         #     loc_b (Tensor): the loc of distribution b.
+        >>>         #     scale_b (Tensor): the scale distribution b.
+        >>>         #     loc_a (Tensor): the loc of distribution a. Default: None. If `loc` is passed in as None,
+        >>>         #         the mean of the underlying Normal distribution will be used.
+        >>>         #     scale_a (Tensor): the scale distribution a. Default: None. If `scale` is passed in as None,
+        >>>         #         the standard deviation of the underlying Normal distribution will be used.
+        >>>
+        >>>         # Examples of `kl_loss`. `cross_entropy` is similar.
+        >>>         ans = self.n1.kl_loss('Normal', loc_b, scale_b)
+        >>>         ans = self.n1.kl_loss('Normal', loc_b, scale_b, loc_a, scale_a)
+        >>>         # Additional `loc` and `scale` must be passed in since they were not passed in construct.
+        >>>         ans = self.n2.kl_loss('Normal', loc_b, scale_b, loc_a, scale_a)
+        >>>
+        >>>         # Examples of `sample`.
+        >>>         # Args:
+        >>>         #     shape (tuple): the shape of the sample. Default: ()
+        >>>         #     loc (Tensor): the loc of the distribution. Default: None. If `loc` is passed in as None,
+        >>>         #         the mean of the underlying Normal distribution will be used.
+        >>>         #     scale (Tensor): the scale of the distribution. Default: None. If `scale` is passed in as None,
+        >>>         #         the standard deviation of the underlying Normal distribution will be used.
+        >>>         ans = self.n1.sample()
+        >>>         ans = self.n1.sample((2,3))
+        >>>         ans = self.n1.sample((2,3), loc_b, scale_b)
+        >>>         ans = self.n2.sample((2,3), loc_a, scale_a)
+    """
+
+    def __init__(self,
+                 loc=None,
+                 scale=None,
+                 seed=0,
+                 dtype=mstype.float32,
+                 name="LogNormal"):
+        """
+        Constructor of LogNormal distribution.
+        """
+        super(LogNormal, self).__init__(distribution=msd.Normal(loc, scale, dtype=dtype),
+                                        bijector=msb.Exp(),
+                                        dtype=dtype, seed=seed, name=name)
+
+        self.log_2pi = np.log(2 * np.pi)
+
+        #ops needed for the class
+        self.exp = exp_generic
+        self.expm1 = expm1_generic
+        self.log = log_generic
+        self.const = P.ScalarToArray()
+        self.erf = P.Erf()
+        self.fill = P.Fill()
+        self.shape = P.Shape()
+        self.sq = P.Square()
+        self.sqrt = P.Sqrt()
+        self.zeroslike = P.ZerosLike()
+
+    @property
+    def loc(self):
+        """Distribution parameter for the pre-transformed mean."""
+        return self.distribution("mean")
+
+    @property
+    def scale(self):
+        """Distribution parameter for the pre-transformed standard deviation."""
+        return self.distribution("sd")
+
+    def extend_repr(self):
+        if self.is_scalar_batch:
+            str_info = f'loc = {self._mean_value}, scale = {self._sd_value}'
+        else:
+            str_info = f'batch_shape = {self._broadcast_shape}'
+        return str_info
+
+    def _mean(self, loc=None, scale=None):
+        """
+        The mean of the distribution.
+        """
+        mean, sd = self._check_param_type(loc, scale)
+        var = self.distribution("var", mean=mean, sd=sd)
+        return self.exp(mean + 0.5 * var)
+
+    def _mode(self, loc=None, scale=None):
+        """
+        The mode of the distribution.
+        """
+        mean, sd = self._check_param_type(loc, scale)
+        var = self.distribution("var", mean=mean, sd=sd)
+        return self.exp(mean - var)
+
+    def _var(self, loc=None, scale=None):
+        """
+        The varience of the distribution.
+        """
+        mean, sd = self._check_param_type(loc, scale)
+        var = self.distribution("var", mean=mean, sd=sd)
+        return self.expm1(var) * self.exp(2. * mean + var)
+
+    def _entropy(self, loc=None, scale=None):
+        r"""
+        Evaluate entropy.
+
+        .. math::
+            H(X) = μ + 0.5 + \log(σ) + 0.5 * \log(2pi)
+        """
+        mean, sd = self._check_param_type(loc, scale)
+        return mean + 0.5 + self.log(sd) + 0.5 * self.log_2pi
+
+    def _cross_entropy(self, dist, loc_b, scale_b, loc_a=None, scale_a=None):
+        r"""
+        Evaluate cross entropy between lognormal distributions.
+
+        Args:
+            dist (str): The type of the distributions. Should be "LogNormal" in this case.
+            loc_b (Tensor): The loc of distribution b.
+            scale_b (Tensor): The scale of distribution b.
+            loc_a (Tensor): The loc of distribution a. Default: None.
+            scale_a (Tensor): The scale of distribution a. Default: None.
+        """
+        check_distribution_name(dist, 'LogNormal')
+        return self._entropy(loc_a, scale_a) + self._kl_loss(dist, loc_b, scale_b, loc_a, scale_a)
+
+    def _kl_loss(self, dist, loc_b, scale_b, loc_a=None, scale_a=None):
+        r"""
+        Evaluate LogNormal-LogNormal kl divergence, i.e. KL(a||b).
+
+        Args:
+            dist (str): The type of the distributions. Should be "LogNormal" in this case.
+            loc_b (Tensor): The loc of distribution b.
+            scale_b (Tensor): The scale of distribution b.
+            loc_a (Tensor): The loc of distribution a. Default: None.
+            scale_a (Tensor): The scale of distribution a. Default: None.
+
+        .. math::
+            KL(a||b) = 0.5 * (\fract{MEAN(a)}{STD(b)} - \fract{MEAN(b)}{STD(b)}) ^ 2 +
+                       0.5 * EXPM1(2 * (\log(STD(a)) - \log(STD(b))) - (\log(STD(a)) - \log(STD(b)))
+        """
+        check_distribution_name(dist, 'LogNormal')
+        return self.distribution("kl_loss", 'Normal', loc_b, scale_b, loc_a, scale_a)
diff --git a/mindspore/nn/probability/distribution/transformed_distribution.py b/mindspore/nn/probability/distribution/transformed_distribution.py
index c47ba7db0b7..a4a91d0832d 100644
--- a/mindspore/nn/probability/distribution/transformed_distribution.py
+++ b/mindspore/nn/probability/distribution/transformed_distribution.py
@@ -30,6 +30,8 @@ class TransformedDistribution(Distribution):
     Args:
         bijector (Bijector): The transformation to perform.
         distribution (Distribution): The original distribution.
+        dtype (mindspore.dtype): The type of the event samples.
+        seed (int): The seed is used in sampling. The global seed is used if it is None.
         name (str): The name of the transformed distribution. Default: 'transformed_distribution'.
 
     Note:
@@ -98,38 +100,38 @@ class TransformedDistribution(Distribution):
     def is_linear_transformation(self):
         return self._is_linear_transformation
 
-    def _cdf(self, *args, **kwargs):
+    def _cdf(self, value, *args, **kwargs):
         r"""
         .. math::
             Y = g(X)
             P(Y <= a) = P(X <= g^{-1}(a))
         """
-        inverse_value = self.bijector("inverse", *args, **kwargs)
-        return self.distribution("cdf", inverse_value)
+        inverse_value = self.bijector("inverse", value)
+        return self.distribution("cdf", inverse_value, *args, **kwargs)
 
-    def _log_cdf(self, *args, **kwargs):
-        return self.log(self._cdf(*args, **kwargs))
+    def _log_cdf(self, value, *args, **kwargs):
+        return self.log(self._cdf(value, *args, **kwargs))
 
-    def _survival_function(self, *args, **kwargs):
-        return 1.0 - self._cdf(*args, **kwargs)
+    def _survival_function(self, value, *args, **kwargs):
+        return 1.0 - self._cdf(value, *args, **kwargs)
 
-    def _log_survival(self, *args, **kwargs):
-        return self.log(self._survival_function(*args, **kwargs))
+    def _log_survival(self, value, *args, **kwargs):
+        return self.log(self._survival_function(value, *args, **kwargs))
 
-    def _log_prob(self, *args, **kwargs):
+    def _log_prob(self, value, *args, **kwargs):
         r"""
         .. math::
             Y = g(X)
             Py(a) = Px(g^{-1}(a)) * (g^{-1})'(a)
             \log(Py(a)) = \log(Px(g^{-1}(a))) + \log((g^{-1})'(a))
         """
-        inverse_value = self.bijector("inverse", *args, **kwargs)
-        unadjust_prob = self.distribution("log_prob", inverse_value)
-        log_jacobian = self.bijector("inverse_log_jacobian", *args, **kwargs)
+        inverse_value = self.bijector("inverse", value)
+        unadjust_prob = self.distribution("log_prob", inverse_value, *args, **kwargs)
+        log_jacobian = self.bijector("inverse_log_jacobian", value)
         return unadjust_prob + log_jacobian
 
-    def _prob(self, *args, **kwargs):
-        return self.exp(self._log_prob(*args, **kwargs))
+    def _prob(self, value, *args, **kwargs):
+        return self.exp(self._log_prob(value, *args, **kwargs))
 
     def _sample(self, *args, **kwargs):
         org_sample = self.distribution("sample", *args, **kwargs)
diff --git a/tests/st/probability/distribution/test_lognormal.py b/tests/st/probability/distribution/test_lognormal.py
new file mode 100644
index 00000000000..5b903852d5d
--- /dev/null
+++ b/tests/st/probability/distribution/test_lognormal.py
@@ -0,0 +1,322 @@
+# Copyright 2019 Huawei Technologies Co., Ltd
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ============================================================================
+"""test cases for LogNormal distribution"""
+import numpy as np
+from scipy import stats
+import mindspore.context as context
+import mindspore.nn as nn
+import mindspore.nn.probability.distribution as msd
+from mindspore import Tensor
+from mindspore import dtype
+
+context.set_context(mode=context.GRAPH_MODE, device_target="Ascend")
+
+class Prob(nn.Cell):
+    """
+    Test class: probability of LogNormal distribution.
+    """
+    def __init__(self):
+        super(Prob, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.ln.prob(x_)
+
+def test_pdf():
+    """
+    Test pdf.
+    """
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_pdf = lognorm_benchmark.pdf([1.0, 2.0]).astype(np.float32)
+    pdf = Prob()
+    output = pdf(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_pdf) < tol).all()
+
+class LogProb(nn.Cell):
+    """
+    Test class: log probability of LogNormal distribution.
+    """
+    def __init__(self):
+        super(LogProb, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.ln.log_prob(x_)
+
+def test_log_likelihood():
+    """
+    Test log_pdf.
+    """
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_logpdf = lognorm_benchmark.logpdf([1.0, 2.0]).astype(np.float32)
+    logprob = LogProb()
+    output = logprob(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_logpdf) < tol).all()
+
+class KL(nn.Cell):
+    """
+    Test class: kl_loss of LogNormal distribution.
+    """
+    def __init__(self):
+        super(KL, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([0.4]), dtype=dtype.float32)
+
+    def construct(self, x_, y_):
+        return self.ln.kl_loss('LogNormal', x_, y_)
+
+def test_kl_loss():
+    """
+    Test kl_loss.
+    """
+    mean_a = np.array([0.3]).astype(np.float32)
+    sd_a = np.array([0.4]).astype(np.float32)
+
+    mean_b = np.array([1.0]).astype(np.float32)
+    sd_b = np.array([1.0]).astype(np.float32)
+
+    diff_log_scale = np.log(sd_a) - np.log(sd_b)
+    squared_diff = np.square(mean_a / sd_b - mean_b / sd_b)
+    expect_kl_loss = 0.5 * squared_diff + 0.5 * np.expm1(2 * diff_log_scale) - diff_log_scale
+
+    kl_loss = KL()
+    mean = Tensor(mean_b, dtype=dtype.float32)
+    sd = Tensor(sd_b, dtype=dtype.float32)
+    output = kl_loss(mean, sd)
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_kl_loss) < tol).all()
+
+class Basics(nn.Cell):
+    """
+    Test class: mean/sd/mode of LogNormal distribution.
+    """
+    def __init__(self):
+        super(Basics, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self):
+        return self.ln.mean(), self.ln.sd(), self.ln.mode()
+
+def test_basics():
+    """
+    Test mean/standard deviation/mode.
+    """
+    basics = Basics()
+    mean, sd, mode = basics()
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_mean = lognorm_benchmark.mean().astype(np.float32)
+    expect_sd = lognorm_benchmark.std().astype(np.float32)
+    expect_mode = (lognorm_benchmark.median() / np.exp(np.square([[0.2], [0.4]]))).astype(np.float32)
+    tol = 1e-6
+    assert (np.abs(mean.asnumpy() - expect_mean) < tol).all()
+    assert (np.abs(mode.asnumpy() - expect_mode) < tol).all()
+    assert (np.abs(sd.asnumpy() - expect_sd) < tol).all()
+
+class Sampling(nn.Cell):
+    """
+    Test class: sample of LogNormal distribution.
+    """
+    def __init__(self, shape, seed=0):
+        super(Sampling, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), seed=seed, dtype=dtype.float32)
+        self.shape = shape
+
+    def construct(self, mean=None, sd=None):
+        return self.ln.sample(self.shape, mean, sd)
+
+def test_sample():
+    """
+    Test sample.
+    """
+    shape = (2, 3)
+    seed = 10
+    mean = Tensor([2.0], dtype=dtype.float32)
+    sd = Tensor([2.0, 2.0, 2.0], dtype=dtype.float32)
+    sample = Sampling(shape, seed=seed)
+    output = sample(mean, sd)
+    assert output.shape == (2, 3, 3)
+
+class CDF(nn.Cell):
+    """
+    Test class: cdf of LogNormal distribution.
+    """
+    def __init__(self):
+        super(CDF, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.ln.cdf(x_)
+
+def test_cdf():
+    """
+    Test cdf.
+    """
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_cdf = lognorm_benchmark.cdf([1.0, 2.0]).astype(np.float32)
+    cdf = CDF()
+    output = cdf(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 2e-5
+    assert (np.abs(output.asnumpy() - expect_cdf) < tol).all()
+
+class LogCDF(nn.Cell):
+    """
+    Test class: log_cdf of Mormal distribution.
+    """
+    def __init__(self):
+        super(LogCDF, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.ln.log_cdf(x_)
+
+def test_log_cdf():
+    """
+    Test log cdf.
+    """
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_logcdf = lognorm_benchmark.logcdf([1.0, 2.0]).astype(np.float32)
+    logcdf = LogCDF()
+    output = logcdf(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 1e-4
+    assert (np.abs(output.asnumpy() - expect_logcdf) < tol).all()
+
+class SF(nn.Cell):
+    """
+    Test class: survival function of LogNormal distribution.
+    """
+    def __init__(self):
+        super(SF, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.ln.survival_function(x_)
+
+def test_survival():
+    """
+    Test log_survival.
+    """
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_survival = lognorm_benchmark.sf([1.0, 2.0]).astype(np.float32)
+    survival_function = SF()
+    output = survival_function(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 2e-5
+    assert (np.abs(output.asnumpy() - expect_survival) < tol).all()
+
+class LogSF(nn.Cell):
+    """
+    Test class: log survival function of LogNormal distribution.
+    """
+    def __init__(self):
+        super(LogSF, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self, x_):
+        return self.ln.log_survival(x_)
+
+def test_log_survival():
+    """
+    Test log_survival.
+    """
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_log_survival = lognorm_benchmark.logsf([1.0, 2.0]).astype(np.float32)
+    log_survival = LogSF()
+    output = log_survival(Tensor([1.0, 2.0], dtype=dtype.float32))
+    tol = 5e-4
+    assert (np.abs(output.asnumpy() - expect_log_survival) < tol).all()
+
+class EntropyH(nn.Cell):
+    """
+    Test class: entropy of LogNormal distribution.
+    """
+    def __init__(self):
+        super(EntropyH, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=dtype.float32)
+
+    def construct(self):
+        return self.ln.entropy()
+
+def test_entropy():
+    """
+    Test entropy.
+    """
+    lognorm_benchmark = stats.lognorm(s=np.array([[0.2], [0.4]]), scale=np.exp(np.array([0.3])))
+    expect_entropy = lognorm_benchmark.entropy().astype(np.float32)
+    entropy = EntropyH()
+    output = entropy()
+    tol = 1e-6
+    assert (np.abs(output.asnumpy() - expect_entropy) < tol).all()
+
+class CrossEntropy(nn.Cell):
+    """
+    Test class: cross entropy between LogNormal distributions.
+    """
+    def __init__(self):
+        super(CrossEntropy, self).__init__()
+        self.ln = msd.LogNormal(np.array([0.3]), np.array([0.4]), dtype=dtype.float32)
+
+    def construct(self, x_, y_):
+        entropy = self.ln.entropy()
+        kl_loss = self.ln.kl_loss('LogNormal', x_, y_)
+        h_sum_kl = entropy + kl_loss
+        cross_entropy = self.ln.cross_entropy('LogNormal', x_, y_)
+        return h_sum_kl - cross_entropy
+
+def test_cross_entropy():
+    """
+    Test cross_entropy.
+    """
+    cross_entropy = CrossEntropy()
+    mean = Tensor([1.0], dtype=dtype.float32)
+    sd = Tensor([1.0], dtype=dtype.float32)
+    diff = cross_entropy(mean, sd)
+    tol = 1e-6
+    assert (np.abs(diff.asnumpy() - np.zeros(diff.shape)) < tol).all()
+
+class Net(nn.Cell):
+    """
+    Test class: expand single distribution instance to multiple graphs
+    by specifying the attributes.
+    """
+
+    def __init__(self):
+        super(Net, self).__init__()
+        self.LogNormal = msd.LogNormal(0., 1., dtype=dtype.float32)
+
+    def construct(self, x_, y_):
+        kl = self.LogNormal.kl_loss('LogNormal', x_, y_)
+        prob = self.LogNormal.prob(kl)
+        return prob
+
+def test_multiple_graphs():
+    """
+    Test multiple graphs case.
+    """
+    prob = Net()
+    mean_a = np.array([0.0]).astype(np.float32)
+    sd_a = np.array([1.0]).astype(np.float32)
+    mean_b = np.array([1.0]).astype(np.float32)
+    sd_b = np.array([1.0]).astype(np.float32)
+    ans = prob(Tensor(mean_b), Tensor(sd_b))
+
+    diff_log_scale = np.log(sd_a) - np.log(sd_b)
+    squared_diff = np.square(mean_a / sd_b - mean_b / sd_b)
+    expect_kl_loss = 0.5 * squared_diff + 0.5 * \
+        np.expm1(2 * diff_log_scale) - diff_log_scale
+    lognorm_benchmark = stats.lognorm(s=np.array([1.]), scale=np.exp(np.array([0.])))
+    expect_prob = lognorm_benchmark.pdf(expect_kl_loss).astype(np.float32)
+
+    tol = 1e-6
+    assert (np.abs(ans.asnumpy() - expect_prob) < tol).all()
diff --git a/tests/ut/python/nn/probability/distribution/test_lognormal.py b/tests/ut/python/nn/probability/distribution/test_lognormal.py
new file mode 100644
index 00000000000..f351fa310f5
--- /dev/null
+++ b/tests/ut/python/nn/probability/distribution/test_lognormal.py
@@ -0,0 +1,216 @@
+# Copyright 2020 Huawei Technologies Co., Ltd
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ============================================================================
+"""
+Test nn.probability.distribution.LogNormal.
+"""
+import numpy as np
+import pytest
+
+import mindspore.nn as nn
+import mindspore.nn.probability.distribution as msd
+from mindspore import dtype
+from mindspore import Tensor
+
+def test_lognormal_shape_errpr():
+    """
+    Invalid shapes.
+    """
+    with pytest.raises(ValueError):
+        msd.LogNormal([[2.], [1.]], [[2.], [3.], [4.]], dtype=dtype.float32)
+
+def test_type():
+    with pytest.raises(TypeError):
+        msd.LogNormal(0., 1., dtype=dtype.int32)
+
+def test_name():
+    with pytest.raises(TypeError):
+        msd.LogNormal(0., 1., name=1.0)
+
+def test_seed():
+    with pytest.raises(TypeError):
+        msd.LogNormal(0., 1., seed='seed')
+
+def test_sd():
+    with pytest.raises(ValueError):
+        msd.LogNormal(0., 0.)
+    with pytest.raises(ValueError):
+        msd.LogNormal(0., -1.)
+
+def test_arguments():
+    """
+    args passing during initialization.
+    """
+    n = msd.LogNormal()
+    assert isinstance(n, msd.Distribution)
+    n = msd.LogNormal([3.0], [4.0], dtype=dtype.float32)
+    assert isinstance(n, msd.Distribution)
+
+
+class LogNormalProb(nn.Cell):
+    """
+    LogNormal distribution: initialize with mean/sd.
+    """
+    def __init__(self):
+        super(LogNormalProb, self).__init__()
+        self.lognormal = msd.LogNormal(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self, value):
+        prob = self.lognormal.prob(value)
+        log_prob = self.lognormal.log_prob(value)
+        cdf = self.lognormal.cdf(value)
+        log_cdf = self.lognormal.log_cdf(value)
+        sf = self.lognormal.survival_function(value)
+        log_sf = self.lognormal.log_survival(value)
+        return prob + log_prob + cdf + log_cdf + sf + log_sf
+
+def test_lognormal_prob():
+    """
+    Test probability functions: passing value through construct.
+    """
+    net = LogNormalProb()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    ans = net(value)
+    assert isinstance(ans, Tensor)
+
+
+class LogNormalProb1(nn.Cell):
+    """
+    LogNormal distribution: initialize without mean/sd.
+    """
+    def __init__(self):
+        super(LogNormalProb1, self).__init__()
+        self.lognormal = msd.LogNormal()
+
+    def construct(self, value, mean, sd):
+        prob = self.lognormal.prob(value, mean, sd)
+        log_prob = self.lognormal.log_prob(value, mean, sd)
+        cdf = self.lognormal.cdf(value, mean, sd)
+        log_cdf = self.lognormal.log_cdf(value, mean, sd)
+        sf = self.lognormal.survival_function(value, mean, sd)
+        log_sf = self.lognormal.log_survival(value, mean, sd)
+        return prob + log_prob + cdf + log_cdf + sf + log_sf
+
+def test_lognormal_prob1():
+    """
+    Test probability functions: passing mean/sd, value through construct.
+    """
+    net = LogNormalProb1()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    mean = Tensor([0.0], dtype=dtype.float32)
+    sd = Tensor([1.0], dtype=dtype.float32)
+    ans = net(value, mean, sd)
+    assert isinstance(ans, Tensor)
+
+class LogNormalKl(nn.Cell):
+    """
+    Test class: kl_loss of LogNormal distribution.
+    """
+    def __init__(self):
+        super(LogNormalKl, self).__init__()
+        self.n1 = msd.LogNormal(np.array([3.0]), np.array([4.0]), dtype=dtype.float32)
+        self.n2 = msd.LogNormal(dtype=dtype.float32)
+
+    def construct(self, mean_b, sd_b, mean_a, sd_a):
+        kl1 = self.n1.kl_loss('LogNormal', mean_b, sd_b)
+        kl2 = self.n2.kl_loss('LogNormal', mean_b, sd_b, mean_a, sd_a)
+        return kl1 + kl2
+
+def test_kl():
+    """
+    Test kl_loss.
+    """
+    net = LogNormalKl()
+    mean_b = Tensor(np.array([1.0]).astype(np.float32), dtype=dtype.float32)
+    sd_b = Tensor(np.array([1.0]).astype(np.float32), dtype=dtype.float32)
+    mean_a = Tensor(np.array([2.0]).astype(np.float32), dtype=dtype.float32)
+    sd_a = Tensor(np.array([3.0]).astype(np.float32), dtype=dtype.float32)
+    ans = net(mean_b, sd_b, mean_a, sd_a)
+    assert isinstance(ans, Tensor)
+
+class LogNormalCrossEntropy(nn.Cell):
+    """
+    Test class: cross_entropy of LogNormal distribution.
+    """
+    def __init__(self):
+        super(LogNormalCrossEntropy, self).__init__()
+        self.n1 = msd.LogNormal(np.array([3.0]), np.array([4.0]), dtype=dtype.float32)
+        self.n2 = msd.LogNormal(dtype=dtype.float32)
+
+    def construct(self, mean_b, sd_b, mean_a, sd_a):
+        h1 = self.n1.cross_entropy('LogNormal', mean_b, sd_b)
+        h2 = self.n2.cross_entropy('LogNormal', mean_b, sd_b, mean_a, sd_a)
+        return h1 + h2
+
+def test_cross_entropy():
+    """
+    Test cross entropy between LogNormal distributions.
+    """
+    net = LogNormalCrossEntropy()
+    mean_b = Tensor(np.array([1.0]).astype(np.float32), dtype=dtype.float32)
+    sd_b = Tensor(np.array([1.0]).astype(np.float32), dtype=dtype.float32)
+    mean_a = Tensor(np.array([2.0]).astype(np.float32), dtype=dtype.float32)
+    sd_a = Tensor(np.array([3.0]).astype(np.float32), dtype=dtype.float32)
+    ans = net(mean_b, sd_b, mean_a, sd_a)
+    assert isinstance(ans, Tensor)
+
+class LogNormalBasics(nn.Cell):
+    """
+    Test class: basic mean/sd function.
+    """
+    def __init__(self):
+        super(LogNormalBasics, self).__init__()
+        self.n = msd.LogNormal(3.0, 4.0, dtype=dtype.float32)
+
+    def construct(self):
+        mean = self.n.mean()
+        sd = self.n.sd()
+        mode = self.n.mode()
+        entropy = self.n.entropy()
+        return mean + sd + mode + entropy
+
+def test_bascis():
+    """
+    Test mean/sd/mode/entropy functionality of LogNormal.
+    """
+    net = LogNormalBasics()
+    ans = net()
+    assert isinstance(ans, Tensor)
+
+
+class LogNormalConstruct(nn.Cell):
+    """
+    LogNormal distribution: going through construct.
+    """
+    def __init__(self):
+        super(LogNormalConstruct, self).__init__()
+        self.lognormal = msd.LogNormal(3.0, 4.0)
+        self.lognormal1 = msd.LogNormal()
+
+    def construct(self, value, mean, sd):
+        prob = self.lognormal('prob', value)
+        prob1 = self.lognormal('prob', value, mean, sd)
+        prob2 = self.lognormal1('prob', value, mean, sd)
+        return prob + prob1 + prob2
+
+def test_lognormal_construct():
+    """
+    Test probability function going through construct.
+    """
+    net = LogNormalConstruct()
+    value = Tensor([0.5, 1.0], dtype=dtype.float32)
+    mean = Tensor([0.0], dtype=dtype.float32)
+    sd = Tensor([1.0], dtype=dtype.float32)
+    ans = net(value, mean, sd)
+    assert isinstance(ans, Tensor)