diff --git a/paddle/operators/norm_op.cc b/paddle/operators/norm_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..3835da630d2142b20134b6554f268824d4718752
--- /dev/null
+++ b/paddle/operators/norm_op.cc
@@ -0,0 +1,106 @@
+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserve.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+Indicesou 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. */
+
+#include "paddle/operators/norm_op.h"
+namespace paddle {
+namespace operators {
+
+class NormOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  NormOpMaker(framework::OpProto* proto, framework::OpAttrChecker* op_checker)
+      : OpProtoAndCheckerMaker(proto, op_checker) {
+    AddInput(
+        "X",
+        "(Tensor) The input tensor of norm operator. "
+        "The format of input tensor is NCHW. Where N is batch size, C is the "
+        "number of channels, H and W is the height and width of feature.");
+    AddInput("Scale",
+             "(Tensor) The input tensor of norm operator. "
+             "The format of input tensor is C * 1.");
+    AddAttr<float>("epsilon",
+                   "(float, default 1e-10) Constant "
+                   "for numerical stability.")
+        .SetDefault(1.0e-10f);
+    AddOutput("Out",
+              "(Tensor) The output tensor of norm operator."
+              "N * M."
+              "M = C * H * W");
+    AddComment(R"DOC(
+       "Input shape: $(N, C, H, W)$
+        Sclae shape: $(C, 1)$
+        Output shape: $(N, C, H, W)$
+        Where
+        forward
+          $$
+            [\frac {x_{1}}{\sqrt{\sum{x_{i}^{2}}}} \frac {x_{2}}{\sqrt{\sum{x_{i}^{2}}}} \frac {x_{3}}{\sqrt{\sum{x_{i}^{2}}}} \cdot  \cdot  \cdot \frac {x_{n}}{\sqrt{\sum{x_{i}^{2}}}}]
+          $$
+        backward
+          $$
+            \frac{\frac{\mathrm{d}L }{\mathrm{d}y_{1}} - \frac {x_{1}\sum {\frac{\mathrm{d} L}{\mathrm{d} y_{j}}}x_{j}}{\sum x_{j}^{2}} }{\sqrt{\sum{x_{j}^{2}}}}
+          $$
+        )DOC");
+  }
+};
+
+class NormOp : public framework::OperatorWithKernel {
+ protected:
+  framework::OpKernelType GetKernelType(
+      const framework::ExecutionContext& ctx) const override {
+    return framework::OpKernelType(
+        framework::ToDataType(ctx.Input<framework::Tensor>("X")->type()),
+        ctx.device_context());
+  }
+
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+  void InferShape(framework::InferShapeContext* ctx) const override {
+    PADDLE_ENFORCE(ctx->HasInput("X"),
+                   "Input(X) of NormOp"
+                   "should not be null.");
+    PADDLE_ENFORCE(ctx->HasOutput("Out"),
+                   "Output(Out) of NormOp should not be null.");
+    auto in_x_dims = ctx->GetInputDim("X");
+    ctx->SetOutputDim("Out", in_x_dims);
+  }
+};
+
+class NormOpGrad : public framework::OperatorWithKernel {
+ protected:
+  framework::OpKernelType GetKernelType(
+      const framework::ExecutionContext& ctx) const override {
+    return framework::OpKernelType(
+        framework::ToDataType(ctx.Input<framework::Tensor>("X")->type()),
+        ctx.device_context());
+  }
+
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+  void InferShape(framework::InferShapeContext* ctx) const override {
+    PADDLE_ENFORCE(ctx->HasInput("X"), "Input(X) must not be null.");
+    PADDLE_ENFORCE(ctx->HasOutput(framework::GradVarName("X")),
+                   "Input(X@GRAD) should not be null.");
+    ctx->SetOutputDim(framework::GradVarName("X"), ctx->GetInputDim("X"));
+  }
+};
+}  // namespace operators
+}  // namespace paddle
+
+namespace ops = paddle::operators;
+REGISTER_OP(norm, ops::NormOp, ops::NormOpMaker, norm_grad, ops::NormOpGrad);
+REGISTER_OP_CPU_KERNEL(
+    norm, ops::NormKernel<paddle::platform::CPUDeviceContext, float>,
+    ops::NormKernel<paddle::platform::CPUDeviceContext, double>);
+REGISTER_OP_CPU_KERNEL(
+    norm_grad, ops::NormGradKernel<paddle::platform::CPUDeviceContext, float>,
+    ops::NormGradKernel<paddle::platform::CPUDeviceContext, double>);
diff --git a/paddle/operators/norm_op.cu b/paddle/operators/norm_op.cu
new file mode 100644
index 0000000000000000000000000000000000000000..7d84aaa73248d6bbf1cf104105ce2a2847000eea
--- /dev/null
+++ b/paddle/operators/norm_op.cu
@@ -0,0 +1,24 @@
+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserve.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+Indicesou 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. */
+#define EIGEN_USE_GPU
+
+#include "paddle/operators/norm_op.h"
+
+namespace ops = paddle::operators;
+REGISTER_OP_CUDA_KERNEL(
+    norm, ops::NormKernel<paddle::platform::CUDADeviceContext, float>,
+    ops::NormKernel<paddle::platform::CUDADeviceContext, double>);
+REGISTER_OP_CUDA_KERNEL(
+    norm_grad, ops::NormGradKernel<paddle::platform::CUDADeviceContext, float>,
+    ops::NormGradKernel<paddle::platform::CUDADeviceContext, double>);
diff --git a/paddle/operators/norm_op.h b/paddle/operators/norm_op.h
new file mode 100644
index 0000000000000000000000000000000000000000..d3dcf4834162f7a57c9a33b51736e8f4d4446134
--- /dev/null
+++ b/paddle/operators/norm_op.h
@@ -0,0 +1,162 @@
+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserve.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+Indicesou 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. */
+
+#pragma once
+#include "paddle/framework/op_registry.h"
+#include "paddle/operators/math/math_function.h"
+
+namespace paddle {
+namespace operators {
+
+template <typename T, int MajorType = Eigen::RowMajor,
+          typename IndexType = Eigen::DenseIndex>
+using EigenVector = framework::EigenVector<T, MajorType, IndexType>;
+template <typename T, int MajorType = Eigen::RowMajor,
+          typename IndexType = Eigen::DenseIndex>
+using EigenMatrix = framework::EigenMatrix<T, MajorType, IndexType>;
+
+template <typename DeviceContext, typename T>
+class NormKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    const framework::Tensor* in_x = context.Input<framework::Tensor>("X");
+    const framework::Tensor* scale = context.Input<framework::Tensor>("Scale");
+    auto* out = context.Output<framework::Tensor>("Out");
+    T epsilon = context.Attr<T>("epsilon");
+    out->mutable_data<T>(context.GetPlace());
+    int batch_size = in_x->dims()[0];
+    int channels = in_x->dims()[1];
+    int height = in_x->dims()[2];
+    int width = in_x->dims()[3];
+    int fea_len = height * width;
+    auto* place =
+        context.template device_context<DeviceContext>().eigen_device();
+    auto x = EigenMatrix<T>::From(
+        *in_x, framework::make_ddim({batch_size, fea_len * channels}));
+    // get square
+    framework::Tensor x_square;
+    x_square.mutable_data<T>(in_x->dims(), context.GetPlace());
+    auto x_square_eigen = EigenMatrix<T>::From(
+        x_square, framework::make_ddim({batch_size, fea_len * channels}));
+    x_square_eigen.device(*place) = x.square();
+    auto scale_eigen = EigenVector<T>::Flatten(*scale);
+    for (int n = 0; n < batch_size; ++n) {
+      framework::Tensor in_x_batch = in_x->Slice(n, n + 1);
+      auto in_x_batch_eigen = EigenMatrix<T>::From(
+          in_x_batch, framework::make_ddim({channels, fea_len}));
+      framework::Tensor x_square_batch = x_square.Slice(n, n + 1);
+      auto x_square_batch_eigen = EigenMatrix<T>::From(
+          x_square_batch, framework::make_ddim({channels, fea_len}));
+      framework::Tensor out_batch = out->Slice(n, n + 1);
+      auto out_batch_eigen = EigenMatrix<T>::From(
+          out_batch, framework::make_ddim({channels, fea_len}));
+      framework::Tensor tmp_tensor;
+      tmp_tensor.mutable_data<T>(framework::make_ddim({1, fea_len}),
+                                 context.GetPlace());
+      auto tmp = EigenVector<T>::Flatten(tmp_tensor);
+      // get colsum  and sqrt , inverse
+      auto dim = Eigen::array<int, 1>({{0}});
+      tmp.device(*place) = x_square_batch_eigen.sum(dim);
+      tmp.device(*place) = (tmp + epsilon).sqrt().inverse();
+      Eigen::array<int, 2> broadcast_dim_col;
+      broadcast_dim_col[1] = 1;
+      broadcast_dim_col[0] = channels;
+      out_batch_eigen.device(*place) =
+          in_x_batch_eigen * (tmp.broadcast(broadcast_dim_col));
+      Eigen::array<int, 2> broadcast_dim_row;
+      broadcast_dim_row[1] = fea_len;
+      broadcast_dim_row[0] = 1;
+      out_batch_eigen.device(*place) =
+          out_batch_eigen * (scale_eigen.broadcast(broadcast_dim_row));
+    }
+  }
+};
+template <typename DeviceContext, typename T>
+class NormGradKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    const framework::Tensor* in_x = context.Input<framework::Tensor>("X");
+    const framework::Tensor* scale = context.Input<framework::Tensor>("Scale");
+    const framework::Tensor* out_grad =
+        context.Input<framework::Tensor>(framework::GradVarName("Out"));
+    T epsilon = context.Attr<T>("epsilon");
+    framework::Tensor* in_x_grad =
+        context.Output<framework::Tensor>(framework::GradVarName("X"));
+    in_x_grad->mutable_data<T>(context.GetPlace());
+    int batch_size = in_x->dims()[0];
+    int channels = in_x->dims()[1];
+    int height = in_x->dims()[2];
+    int width = in_x->dims()[3];
+    int fea_len = height * width;
+    auto* place =
+        context.template device_context<DeviceContext>().eigen_device();
+
+    auto scale_eigen = EigenVector<T>::Flatten(*scale);
+    auto x = EigenMatrix<T>::From(
+        *in_x, framework::make_ddim({batch_size, fea_len * channels}));
+    // get square
+    framework::Tensor x_square;
+    x_square.mutable_data<T>(in_x->dims(), context.GetPlace());
+    auto x_square_eigen = EigenMatrix<T>::From(
+        x_square, framework::make_ddim({batch_size, fea_len * channels}));
+    x_square_eigen.device(*place) = x.square();
+
+    for (int n = 0; n < batch_size; ++n) {
+      framework::Tensor in_x_batch = in_x->Slice(n, n + 1);
+      auto in_x_batch_eigen = EigenMatrix<T>::From(
+          in_x_batch, framework::make_ddim({channels, fea_len}));
+      framework::Tensor in_g_batch = in_x_grad->Slice(n, n + 1);
+      auto in_g_batch_eigen = EigenMatrix<T>::From(
+          in_g_batch, framework::make_ddim({channels, fea_len}));
+      framework::Tensor x_square_batch = x_square.Slice(n, n + 1);
+      auto x_square_batch_eigen = EigenMatrix<T>::From(
+          x_square_batch, framework::make_ddim({channels, fea_len}));
+      framework::Tensor outg_batch = out_grad->Slice(n, n + 1);
+      auto outg_batch_eigen = EigenMatrix<T>::From(
+          outg_batch, framework::make_ddim({channels, fea_len}));
+
+      framework::Tensor tmp_tensor;
+      tmp_tensor.mutable_data<T>(framework::make_ddim({1, fea_len}),
+                                 context.GetPlace());
+      auto tmp_eigen = EigenVector<T>::Flatten(tmp_tensor);
+      auto dim = Eigen::array<int, 1>({{0}});
+      tmp_eigen.device(*place) = (in_x_batch_eigen * outg_batch_eigen).sum(dim);
+      framework::Tensor norm_tmp_tensor;
+      norm_tmp_tensor.mutable_data<T>(framework::make_ddim({1, fea_len}),
+                                      context.GetPlace());
+      auto norm_tmp_eigen = EigenVector<T>::Flatten(norm_tmp_tensor);
+      norm_tmp_eigen.device(*place) =
+          (x_square_batch_eigen.sum(dim) + epsilon).sqrt();
+      Eigen::array<int, 2> broadcast_dim_col;
+      broadcast_dim_col[1] = 1;
+      broadcast_dim_col[0] = channels;
+      in_g_batch_eigen.device(*place) =
+          in_x_batch_eigen * tmp_eigen.broadcast(broadcast_dim_col);
+      in_g_batch_eigen.device(*place) =
+          in_g_batch_eigen /
+          (norm_tmp_eigen * norm_tmp_eigen).broadcast(broadcast_dim_col);
+      in_g_batch_eigen.device(*place) = outg_batch_eigen - in_g_batch_eigen;
+      // outg_batch_eigen + (in_g_batch_eigen * -1);
+      in_g_batch_eigen.device(*place) =
+          in_g_batch_eigen / norm_tmp_eigen.broadcast(broadcast_dim_col);
+      Eigen::array<int, 2> broadcast_dim_row;
+      broadcast_dim_row[1] = fea_len;
+      broadcast_dim_row[0] = 1;
+      in_g_batch_eigen.device(*place) =
+          in_g_batch_eigen * (scale_eigen.broadcast(broadcast_dim_row));
+    }
+  }
+};
+}  // namespace operators
+}  // namespace paddle
diff --git a/python/paddle/v2/fluid/tests/test_norm_op.py b/python/paddle/v2/fluid/tests/test_norm_op.py
new file mode 100644
index 0000000000000000000000000000000000000000..23e6841b916a6a26f3c1b4ec4a2569e70e2fdbf9
--- /dev/null
+++ b/python/paddle/v2/fluid/tests/test_norm_op.py
@@ -0,0 +1,57 @@
+import unittest
+import numpy as np
+from op_test import OpTest
+
+
+def norm(input, scale, epsilon):
+    s0, s1, s2, s3 = input.shape
+    x_square = input * input
+    for i in xrange(s0):
+        input_batch = input[i:i + 1, :, :, :]
+        input_batch = input_batch.reshape(s1, s2 * s3)
+        x_square_batch = x_square[i:i + 1, :, :, :]
+        x_square_batch = x_square_batch.reshape(s1, s2 * s3)
+        square_colsum = x_square_batch.sum(axis=0) + epsilon
+        tmp = pow(square_colsum, 0.5)
+        tmp = np.reciprocal(tmp)
+        tmp_tile = np.tile(tmp, s1)
+        tmp_tile = tmp_tile.reshape(s1, s2 * s3)
+        scale_tile = np.tile(scale, (1, s2 * s3))
+        scale_tile = scale_tile.reshape(s1, s2 * s3)
+        out_batch = input_batch * tmp_tile * scale_tile
+        out_batch = out_batch.reshape(1, s1, s2, s3)
+        if i == 0:
+            out = out_batch
+        else:
+            out = np.concatenate((out, out_batch), 0)
+    out.reshape(s0, s1, s2, s3)
+    return out
+
+
+class TestNormOp(OpTest):
+    def setUp(self):
+        self.op_type = "norm"
+        self.init_test_case()
+        input = np.random.random(self.shape).astype("float32")
+        scale = np.array([10, 10, 10])
+        self.inputs = {
+            'X': input.astype('float32'),
+            'Scale': scale.astype('float32')
+        }
+        self.attrs = {'epsilon': self.epsilon}
+        output = norm(input, scale, self.epsilon)
+        self.outputs = {'Out': output.astype('float32')}
+
+    def test_check_output(self):
+        self.check_output()
+
+    def test_check_grad(self):
+        self.check_grad(['X'], 'Out')
+
+    def init_test_case(self):
+        self.shape = [1, 3, 2, 2]
+        self.epsilon = 1e-6
+
+
+if __name__ == '__main__':
+    unittest.main()