diff --git a/mindspore/nn/layer/basic.py b/mindspore/nn/layer/basic.py
index 1c54ba32f85..b03511a25da 100644
--- a/mindspore/nn/layer/basic.py
+++ b/mindspore/nn/layer/basic.py
@@ -455,7 +455,7 @@ class Norm(Cell):
         TypeError: If `keep_dims` is not a bool.
 
     Supported Platforms:
-        ``Ascend`` ``GPU``
+        ``Ascend`` ``GPU`` ``CPU``
 
     Examples:
         >>> net = nn.Norm(axis=0)
diff --git a/tests/st/ops/cpu/test_norm_op.py b/tests/st/ops/cpu/test_norm_op.py
new file mode 100644
index 00000000000..7d2bcb5ac85
--- /dev/null
+++ b/tests/st/ops/cpu/test_norm_op.py
@@ -0,0 +1,58 @@
+# Copyright 2021 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.
+# ============================================================================
+
+import numpy as np
+import pytest
+
+import mindspore
+import mindspore.context as context
+import mindspore.nn as nn
+from mindspore import Tensor
+from mindspore.common.api import ms_function
+
+context.set_context(device_target='CPU')
+
+class NetNorm(nn.Cell):
+    def __init__(self):
+        super(NetNorm, self).__init__()
+
+        self.norm_1 = nn.Norm(axis=0)
+        self.norm_2 = nn.Norm(axis=1)
+        self.norm_3 = nn.Norm(axis=-1)
+        self.norm_4 = nn.Norm(axis=-1, keep_dims=True)
+
+    @ms_function
+    def construct(self, indices):
+        return (self.norm_1(indices),
+                self.norm_2(indices),
+                self.norm_3(indices),
+                self.norm_4(indices))
+
+@pytest.mark.level0
+@pytest.mark.platform_x86_gpu_training
+@pytest.mark.env_onecard
+def test_norm():
+    norm = NetNorm()
+    indices = Tensor(np.array([[4, 4, 9, 1], [2, 1, 3, 6]]), mindspore.float32)
+    output = norm(indices)
+    expect_0 = np.array([4.472136, 4.1231055, 9.486833, 6.0827627]).astype(np.float32)
+    expect_1 = np.array([10.677078, 7.071068]).astype(np.float32)
+    expect_2 = np.array([10.677078, 7.071068]).astype(np.float32)
+    expect_3 = np.array([[10.677078], [7.071068]]).astype(np.float32)
+
+    assert (output[0].asnumpy() == expect_0).all()
+    assert (output[1].asnumpy() == expect_1).all()
+    assert (output[2].asnumpy() == expect_2).all()
+    assert (output[3].asnumpy() == expect_3).all()