diff --git a/mindspore/ccsrc/plugin/device/cpu/kernel/nnacl/fp32_grad/batch_norm.c b/mindspore/ccsrc/plugin/device/cpu/kernel/nnacl/fp32_grad/batch_norm.c
index 122e7116f4f..ebc2133beaf 100644
--- a/mindspore/ccsrc/plugin/device/cpu/kernel/nnacl/fp32_grad/batch_norm.c
+++ b/mindspore/ccsrc/plugin/device/cpu/kernel/nnacl/fp32_grad/batch_norm.c
@@ -53,11 +53,14 @@ void backwardAll(const float *restrict in, const float *restrict yt, const float
     for (int c = 0; c < ch; c++) {
       int ix = i * ch + c;
       dbias[c] += yt[ix];
-      // dscale
-      float x_hat = (in[ix] - mean[c]) * invar[c];
+      // in fact, x_hat should also mul invar[c]. now put this step to the end.
+      float x_hat = in[ix] - mean[c];
       dscale[c] += (yt[ix] * x_hat);
     }
   }
+  for (int c = 0; c < ch; c++) {
+    dscale[c] *= invar[c];
+  }
   backwardComputeDx(in, yt, mean, invar, scale, size, ch, dbias, dscale, dx, N, is_train);
 }
 
@@ -73,11 +76,14 @@ void backwardP1(const float *restrict in, const float *restrict yt, const float
     for (int c = 0; c < ch; c++) {
       int ix = i * ch + c;
       dbias[c] += yt[ix];
-      // dscale
-      float x_hat = (in[ix] - mean[c]) * invar[c];
+      // in fact, x_hat should also mul invar[c]. now put this step to the end.
+      float x_hat = in[ix] - mean[c];
       dscale[c] += (yt[ix] * x_hat);
     }
   }
+  for (int c = 0; c < ch; c++) {
+    dscale[c] *= invar[c];
+  }
 }
 
 #ifdef _MSC_VER
diff --git a/mindspore/lite/src/runtime/kernel/arm/fp32_grad/bn_grad.cc b/mindspore/lite/src/runtime/kernel/arm/fp32_grad/bn_grad.cc
index ab840929331..e84ef8d9075 100644
--- a/mindspore/lite/src/runtime/kernel/arm/fp32_grad/bn_grad.cc
+++ b/mindspore/lite/src/runtime/kernel/arm/fp32_grad/bn_grad.cc
@@ -70,6 +70,7 @@ int BNGradCPUKernel::DoExecute(int task_id) {
     input_var = in_tensors_.at(5);
   }
   auto bn_param = reinterpret_cast<BNGradParameter *>(op_parameter_);
+  CHECK_NULL_RETURN(bn_param);
   int stage = stage_;
   int thread_num = thread_num_;
   float *save_mean = reinterpret_cast<float *>(input_mean->MutableData());
@@ -126,7 +127,8 @@ int BNGradCPUKernel::DoExecute(int task_id) {
         }
       }
       if (thread_num == 1) {
-        backwardAll(x, yt, save_mean, save_var, scale, total, channels, dbias, dscale, dx, (IsTrain()));
+        backwardAll(x, yt, save_mean, save_var, scale, total, channels, dbias, dscale, dx,
+                    (IsTrain() && bn_param->is_training_));
       }
       break;
     }
@@ -136,7 +138,8 @@ int BNGradCPUKernel::DoExecute(int task_id) {
     }
     case 2: {
       backwardP2(x + task_id * stride * channels, yt + task_id * stride * channels, save_mean, save_var, dscale, dbias,
-                 scale, count, total, channels, dx + task_id * stride * channels, (IsTrain()));
+                 scale, count, total, channels, dx + task_id * stride * channels,
+                 (IsTrain() && bn_param->is_training_));
       break;
     }
     default:
diff --git a/mindspore/lite/tools/converter/import/primitive_adjust.cc b/mindspore/lite/tools/converter/import/primitive_adjust.cc
index e6b2f5f64bc..ba7deae719a 100644
--- a/mindspore/lite/tools/converter/import/primitive_adjust.cc
+++ b/mindspore/lite/tools/converter/import/primitive_adjust.cc
@@ -583,6 +583,26 @@ int MoveAttrBatchNorm(const CNodePtr &cnode) {
   value_node->set_value(dst_prim_c);
   return lite::RET_OK;
 }
+
+int MoveAttrMapBatchNormGrad(const CNodePtr &cnode) {
+  MS_ASSERT(cnode != nullptr);
+  auto value_node = cnode->input(0)->cast<ValueNodePtr>();
+  MS_CHECK_TRUE_MSG(value_node != nullptr, RET_NULL_PTR, "value_node is nullptr");
+  auto src_prim = GetValueNode<PrimitivePtr>(value_node);
+  MS_CHECK_TRUE_MSG(src_prim != nullptr, RET_NULL_PTR, "value_node is nullptr");
+  auto dst_prim = std::make_shared<ops::BatchNormGrad>();
+  MS_CHECK_TRUE_MSG(dst_prim != nullptr, RET_NULL_PTR, "dst_prim is nullptr.");
+  auto dst_prim_c = dst_prim->GetPrim();
+  MS_CHECK_TRUE_MSG(dst_prim_c != nullptr, RET_NULL_PTR, "dst_prim_c is nullptr.");
+  dst_prim_c->SetAttrs(src_prim->attrs());
+  auto is_training_attr = src_prim->GetAttr(ops::kIsTraining);
+  if (is_training_attr == nullptr) {
+    MS_LOG(INFO) << "no \"is_training\" attr found in BatchNormGrad, will set it to true by default.";
+    dst_prim->set_is_training(true);
+  }
+  value_node->set_value(dst_prim_c);
+  return lite::RET_OK;
+}
 }  // namespace
 
 bool PrimitiveAdjust::Run(const FuncGraphPtr &func_graphs) {
@@ -665,8 +685,8 @@ REGIST_PRIMITIVE_ADJUST(kNameElu, MoveAttrMapActivation)
 REGIST_PRIMITIVE_ADJUST(kNameEluGrad, MoveAttrMapActivationGrad)
 REGIST_PRIMITIVE_ADJUST(kNameExp, MoveAttrMapCommon<ops::ExpFusion>)
 REGIST_PRIMITIVE_ADJUST(kNameFusedBatchNormEx, MoveAttrMapCommon<ops::FusedBatchNorm>)
-REGIST_PRIMITIVE_ADJUST(kNameFusedBatchNormGradEx, MoveAttrMapCommon<ops::BatchNormGrad>)
-REGIST_PRIMITIVE_ADJUST(kNameFusedBatchNormGradCPU, MoveAttrMapCommon<ops::BatchNormGrad>)
+REGIST_PRIMITIVE_ADJUST(kNameFusedBatchNormGradEx, MoveAttrMapBatchNormGrad)
+REGIST_PRIMITIVE_ADJUST(kNameFusedBatchNormGradCPU, MoveAttrMapBatchNormGrad)
 REGIST_PRIMITIVE_ADJUST(kNameGeLU, MoveAttrMapActivation)
 REGIST_PRIMITIVE_ADJUST(kNameGeLUGrad, MoveAttrMapActivationGrad)
 REGIST_PRIMITIVE_ADJUST(kNameHSigmoid, MoveAttrMapActivation)