diff --git a/paddle/fluid/operators/lgamma_op.cc b/paddle/fluid/operators/lgamma_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..148fb05afcfd9a4ef1fcbc587a2bd33947a41000
--- /dev/null
+++ b/paddle/fluid/operators/lgamma_op.cc
@@ -0,0 +1,99 @@
+// Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
+//
+// 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.
+
+#include "paddle/fluid/operators/lgamma_op.h"
+
+namespace paddle {
+namespace operators {
+
+class LgammaOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddInput("X", "(Tensor), The input tensor of lgamma op.");
+    AddOutput("Out", "(Tensor), The output tensor of lgamma op.");
+    AddComment(R"DOC(
+Lgamma Operator.
+
+This operator performs elementwise lgamma for input $X$.
+$$out = log\Gamma(x)$$
+
+)DOC");
+  }
+};
+
+class LgammaOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+  void InferShape(framework::InferShapeContext* ctx) const override {
+    OP_INOUT_CHECK(ctx->HasInput("X"), "Input", "X", "Lgamma");
+    OP_INOUT_CHECK(ctx->HasOutput("Out"), "Output", "Out", "Lgamma");
+
+    auto in_dims = ctx->GetInputDim("X");
+
+    ctx->SetOutputDim("Out", in_dims);
+    ctx->ShareLoD("X", "Out");
+  }
+};
+
+template <typename T>
+class LgammaGradMaker : public framework::SingleGradOpMaker<T> {
+ public:
+  using framework::SingleGradOpMaker<T>::SingleGradOpMaker;
+
+  void Apply(GradOpPtr<T> retv) const override {
+    retv->SetType("lgamma_grad");
+    retv->SetInput(framework::GradVarName("Out"), this->OutputGrad("Out"));
+    retv->SetInput("X", this->Input("X"));
+    retv->SetAttrMap(this->Attrs());
+    retv->SetOutput(framework::GradVarName("X"), this->InputGrad("X"));
+  }
+};
+
+class LgammaGradOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+  void InferShape(framework::InferShapeContext* ctx) const override {
+    OP_INOUT_CHECK(ctx->HasInput(framework::GradVarName("Out")), "Input",
+                   "Out@Grad", "LgammaGrad");
+    OP_INOUT_CHECK(ctx->HasInput("X"), "Input", "X", "LgammaGrad");
+    OP_INOUT_CHECK(ctx->HasOutput(framework::GradVarName("X")), "Output",
+                   "X@Grad", "LgammaGrad");
+
+    auto dout_dims = ctx->GetInputDim(framework::GradVarName("Out"));
+    ctx->SetOutputDim(framework::GradVarName("X"), dout_dims);
+    ctx->ShareLoD(framework::GradVarName("Out"), framework::GradVarName("X"));
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+namespace ops = paddle::operators;
+
+REGISTER_OPERATOR(lgamma, ops::LgammaOp, ops::LgammaOpMaker,
+                  ops::LgammaGradMaker<paddle::framework::OpDesc>,
+                  ops::LgammaGradMaker<paddle::imperative::OpBase>);
+
+REGISTER_OPERATOR(lgamma_grad, ops::LgammaGradOp);
+
+REGISTER_OP_CPU_KERNEL(
+    lgamma, ops::LgammaKernel<paddle::platform::CPUDeviceContext, float>,
+    ops::LgammaKernel<paddle::platform::CPUDeviceContext, double>)
+
+REGISTER_OP_CPU_KERNEL(
+    lgamma_grad,
+    ops::LgammaGradKernel<paddle::platform::CPUDeviceContext, float>,
+    ops::LgammaGradKernel<paddle::platform::CPUDeviceContext, double>);
diff --git a/paddle/fluid/operators/lgamma_op.cu b/paddle/fluid/operators/lgamma_op.cu
new file mode 100644
index 0000000000000000000000000000000000000000..befd31e3bd8b1898ad6c59dca80dac3ae6de339d
--- /dev/null
+++ b/paddle/fluid/operators/lgamma_op.cu
@@ -0,0 +1,64 @@
+// Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
+//
+// 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.
+
+#include <unsupported/Eigen/SpecialFunctions>
+#include "paddle/fluid/operators/elementwise/elementwise_op_impl.cu.h"
+#include "paddle/fluid/operators/lgamma_op.h"
+#include "paddle/fluid/operators/math/complex_functors.h"
+
+namespace paddle {
+namespace operators {
+
+template <typename T, typename Enable = void>
+struct CudaLgammaFunctor;
+
+template <typename T>
+struct CudaLgammaFunctor<T, math::NoComplex<T, math::Real<T>>> {
+  __device__ __forceinline__ T operator()(const T* args) const {
+    return Eigen::numext::lgamma(args[0]);
+  }
+};
+
+template <typename T>
+class LgammaKernel<platform::CUDADeviceContext, T>
+    : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    const Tensor* x = context.Input<Tensor>("X");
+    Tensor* out = context.Output<Tensor>("Out");
+    out->mutable_data<math::Real<T>>(context.GetPlace());
+
+    auto& dev_ctx = context.device_context<platform::CUDADeviceContext>();
+    std::vector<const framework::Tensor*> ins = {x};
+    std::vector<framework::Tensor*> outs = {out};
+    auto functor = CudaLgammaFunctor<T>();
+    LaunchSameDimsElementwiseCudaKernel<ElementwiseType::kUnary, T,
+                                        math::Real<T>>(dev_ctx, ins, &outs,
+                                                       functor);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+namespace ops = paddle::operators;
+
+REGISTER_OP_CUDA_KERNEL(
+    lgamma, ops::LgammaKernel<paddle::platform::CUDADeviceContext, float>,
+    ops::LgammaKernel<paddle::platform::CUDADeviceContext, double>);
+
+REGISTER_OP_CUDA_KERNEL(
+    lgamma_grad,
+    ops::LgammaGradKernel<paddle::platform::CUDADeviceContext, float>,
+    ops::LgammaGradKernel<paddle::platform::CUDADeviceContext, double>);
diff --git a/paddle/fluid/operators/lgamma_op.h b/paddle/fluid/operators/lgamma_op.h
new file mode 100644
index 0000000000000000000000000000000000000000..674054e74573208ea9bbd537419d202e1a30d8c0
--- /dev/null
+++ b/paddle/fluid/operators/lgamma_op.h
@@ -0,0 +1,100 @@
+// Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
+//
+// 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.
+
+#pragma once
+#include <unsupported/Eigen/SpecialFunctions>
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+#include "paddle/fluid/platform/for_range.h"
+
+namespace paddle {
+namespace operators {
+
+template <typename T>
+struct LgammaFunctor {
+  LgammaFunctor(const T* input, T* output, int64_t numel)
+      : input_(input), output_(output), numel_(numel) {}
+
+  HOSTDEVICE void operator()(int64_t idx) const {
+    output_[idx] = Eigen::numext::lgamma(input_[idx]);
+  }
+
+ private:
+  const T* input_;
+  T* output_;
+  int64_t numel_;
+};
+
+template <typename T>
+struct LgammaGradFunctor {
+  LgammaGradFunctor(const T* dout, const T* x, T* output, int64_t numel)
+      : dout_(dout), x_(x), output_(output), numel_(numel) {}
+
+  HOSTDEVICE void operator()(int64_t idx) const {
+    output_[idx] = dout_[idx] * Eigen::numext::digamma(x_[idx]);
+  }
+
+ private:
+  const T* dout_;
+  const T* x_;
+  T* output_;
+  int64_t numel_;
+};
+
+using Tensor = framework::Tensor;
+
+template <typename DeviceContext, typename T>
+class LgammaKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    const Tensor* x = context.Input<Tensor>("X");
+    Tensor* out = context.Output<Tensor>("Out");
+
+    auto numel = x->numel();
+    auto* x_data = x->data<T>();
+    auto* out_data = out->mutable_data<T>(context.GetPlace(),
+                                          size_t(x->numel() * sizeof(T)));
+
+    auto& dev_ctx = context.template device_context<DeviceContext>();
+    platform::ForRange<DeviceContext> for_range(dev_ctx, numel);
+    LgammaFunctor<T> functor(x_data, out_data, numel);
+    for_range(functor);
+  }
+};
+
+template <typename DeviceContext, typename T>
+class LgammaGradKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& ctx) const {
+    const framework::Tensor* d_out =
+        ctx.Input<framework::Tensor>(framework::GradVarName("Out"));
+    const framework::Tensor* x = ctx.Input<framework::Tensor>("X");
+    framework::Tensor* d_x =
+        ctx.Output<framework::Tensor>(framework::GradVarName("X"));
+
+    auto numel = d_out->numel();
+    auto* dout_data = d_out->data<T>();
+    auto* x_data = x->data<T>();
+    auto* dx_data = d_x->mutable_data<T>(
+        ctx.GetPlace(), static_cast<size_t>(numel * sizeof(T)));
+
+    auto& dev_ctx = ctx.template device_context<DeviceContext>();
+    platform::ForRange<DeviceContext> for_range(dev_ctx, numel);
+    LgammaGradFunctor<T> functor(dout_data, x_data, dx_data, numel);
+    for_range(functor);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
diff --git a/python/paddle/fluid/tests/unittests/test_lgamma_op.py b/python/paddle/fluid/tests/unittests/test_lgamma_op.py
new file mode 100644
index 0000000000000000000000000000000000000000..686d5b1eb6dfefc024ffb435f802dea25fe1d2e0
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_lgamma_op.py
@@ -0,0 +1,56 @@
+# Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
+# 
+# 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 unittest
+import math
+import numpy as np
+import paddle
+from op_test import OpTest
+
+paddle.enable_static()
+
+
+class TestLgammaOp(OpTest):
+    def setUp(self):
+        self.op_type = 'lgamma'
+        self.init_dtype_type()
+        shape = (5, 20)
+        data = np.random.random(shape).astype(self.dtype) + 1
+        self.inputs = {'X': data}
+        result = np.ones(shape).astype(self.dtype)
+        for i in range(shape[0]):
+            for j in range(shape[1]):
+                result[i][j] = math.lgamma(data[i][j])
+        self.outputs = {'Out': result}
+
+    def init_dtype_type(self):
+        self.dtype = np.float64
+
+    def test_check_output(self):
+        self.check_output()
+
+    def test_check_grad_normal(self):
+        self.check_grad(['X'], 'Out', numeric_grad_delta=1e-7)
+
+
+class TestLgammaOpFp32(TestLgammaOp):
+    def init_dtype_type(self):
+        self.dtype = np.float32
+
+    def test_check_grad_normal(self):
+        self.check_grad(['X'], 'Out', numeric_grad_delta=0.005)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/white_list/op_threshold_white_list.py b/python/paddle/fluid/tests/unittests/white_list/op_threshold_white_list.py
index 6076e9dc9f60405c4b5e4dde002191e9f1fdcd5b..c771531b7b61be7933b5355204c532b847b13dc5 100644
--- a/python/paddle/fluid/tests/unittests/white_list/op_threshold_white_list.py
+++ b/python/paddle/fluid/tests/unittests/white_list/op_threshold_white_list.py
@@ -45,6 +45,7 @@ NEED_FIX_FP64_CHECK_GRAD_THRESHOLD_OP_LIST = [
     'bilateral_slice',\
     'cudnn_lstm', \
     'rnn', \
+    'lgamma', \
 ]
 
 NEED_FIX_FP64_CHECK_OUTPUT_THRESHOLD_OP_LIST = ['bilinear_interp',\