diff --git a/paddle/fluid/framework/unused_var_check.cc b/paddle/fluid/framework/unused_var_check.cc
index 0f8465ab8948e..f8ace3e85a643 100644
--- a/paddle/fluid/framework/unused_var_check.cc
+++ b/paddle/fluid/framework/unused_var_check.cc
@@ -75,6 +75,7 @@ static const std::unordered_set<std::string> &GetOpWithUnusedVarAllowSet() {
       "data_norm_grad",                     // 0
       "update_loss_scaling",                // 0
       "fused_embedding_eltwise_layernorm",  // 0
+      "trunc_grad",                         // 1
   });
   return *allow_set;
 }
diff --git a/paddle/fluid/operators/trunc_op.cc b/paddle/fluid/operators/trunc_op.cc
new file mode 100644
index 0000000000000..2b79e2152b2f3
--- /dev/null
+++ b/paddle/fluid/operators/trunc_op.cc
@@ -0,0 +1,89 @@
+/* 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/trunc_op.h"
+
+namespace paddle {
+namespace operators {
+
+class TruncOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+  void InferShape(framework::InferShapeContext *ctx) const override {
+    OP_INOUT_CHECK(ctx->HasInput("X"), "Input", "X", "trunc");
+    OP_INOUT_CHECK(ctx->HasOutput("Out"), "Output", "Out", "trunc");
+    auto input_dims = ctx->GetInputDim("X");
+    ctx->SetOutputDim("Out", input_dims);
+    ctx->ShareLoD("X", /*->*/ "Out");
+  }
+};
+
+class TruncOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddInput("X", "(Tensor), The input tensor of trunc op.");
+    AddOutput("Out", "(Tensor), The output tensor of trunc op.");
+    AddComment(R"DOC(
+Trunc Operator.
+Returns a new tensor with the truncated integer values  of input.
+$$out = trunc(x)$$
+)DOC");
+  }
+};
+
+class TruncGradOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+  void InferShape(framework::InferShapeContext *ctx) const override {
+    OP_INOUT_CHECK(ctx->HasInput(framework::GradVarName("Out")), "Input",
+                   framework::GradVarName("Out"), "TruncGrad");
+    OP_INOUT_CHECK(ctx->HasOutput(framework::GradVarName("X")), "Output",
+                   framework::GradVarName("X"), "TruncGrad");
+
+    auto dout_dims = ctx->GetInputDim(framework::GradVarName("Out"));
+    ctx->SetOutputDim(framework::GradVarName("X"), dout_dims);
+  }
+};
+
+template <typename T>
+class TruncGradOpMaker : public framework::SingleGradOpMaker<T> {
+ public:
+  using framework::SingleGradOpMaker<T>::SingleGradOpMaker;
+
+  void Apply(GradOpPtr<T> retv) const override {
+    retv->SetType("trunc_grad");
+    retv->SetInput(framework::GradVarName("Out"), this->OutputGrad("Out"));
+    retv->SetAttrMap(this->Attrs());
+    retv->SetOutput(framework::GradVarName("X"), this->InputGrad("X"));
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+namespace ops = paddle::operators;
+REGISTER_OPERATOR(trunc, ops::TruncOp, ops::TruncOpMaker,
+                  ops::TruncGradOpMaker<paddle::framework::OpDesc>,
+                  ops::TruncGradOpMaker<paddle::imperative::OpBase>);
+
+REGISTER_OPERATOR(trunc_grad, ops::TruncGradOp);
+
+REGISTER_OP_CPU_KERNEL(trunc, ops::TruncKernel<float>, ops::TruncKernel<double>,
+                       ops::TruncKernel<int>, ops::TruncKernel<int64_t>);
+
+REGISTER_OP_CPU_KERNEL(trunc_grad, ops::TruncGradKernel<float>,
+                       ops::TruncGradKernel<double>, ops::TruncGradKernel<int>,
+                       ops::TruncGradKernel<int64_t>);
diff --git a/paddle/fluid/operators/trunc_op.cu b/paddle/fluid/operators/trunc_op.cu
new file mode 100644
index 0000000000000..a284e0ea6e393
--- /dev/null
+++ b/paddle/fluid/operators/trunc_op.cu
@@ -0,0 +1,115 @@
+/* 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/trunc_op.h"
+#include "paddle/fluid/platform/cuda_primitives.h"
+#include "paddle/fluid/platform/gpu_info.h"
+
+namespace paddle {
+namespace operators {
+
+using platform::PADDLE_CUDA_NUM_THREADS;
+
+template <typename T>
+class TruncFunctor {
+ public:
+  __device__ TruncFunctor(const T x) : x_(x) {}
+  __device__ T operator()() { return trunc(x_); }
+
+ public:
+  const T x_;
+};
+
+template <>
+class TruncFunctor<int> {
+ public:
+  __device__ TruncFunctor(const int x) : x_(x) {}
+  __device__ int operator()() { return x_; }
+
+ public:
+  const int x_;
+};
+
+template <>
+class TruncFunctor<int64_t> {
+ public:
+  __device__ TruncFunctor(const int64_t x) : x_(x) {}
+  __device__ int64_t operator()() { return x_; }
+
+ public:
+  const int64_t x_;
+};
+
+template <typename T>
+__global__ void Trunc(const T* x, T* out, int64_t N) {
+  CUDA_KERNEL_LOOP(index, N) {
+    TruncFunctor<T> functor(x[index]);
+    out[index] = functor();
+  }
+}
+
+template <typename T>
+__global__ void TruncGrad(T* dx, int64_t N) {
+  CUDA_KERNEL_LOOP(index, N) { dx[index] = static_cast<T>(0.0); }
+}
+
+template <typename T>
+class TruncCUDAKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    auto* x = context.Input<Tensor>("X");
+    auto* out = context.Output<Tensor>("Out");
+
+    const auto* x_data = x->data<T>();
+    auto* out_data = out->mutable_data<T>(context.GetPlace());
+
+    int64_t numel = x->numel();
+
+    int theads = PADDLE_CUDA_NUM_THREADS;
+    int blocks = (numel + theads - 1) / theads;
+
+    Trunc<<<blocks, theads>>>(x_data, out_data, numel);
+  }
+};
+
+template <typename T>
+class TruncCUDAGradKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    auto* dout = context.Input<Tensor>(framework::GradVarName("Out"));
+    auto* dx = context.Output<Tensor>(framework::GradVarName("X"));
+
+    const auto* dout_data = dout->data<T>();
+    auto* dx_data = dx->mutable_data<T>(context.GetPlace());
+
+    int64_t numel = dout->numel();
+
+    int theads = PADDLE_CUDA_NUM_THREADS;
+    int blocks = (numel + theads - 1) / theads;
+
+    TruncGrad<<<blocks, theads>>>(dx_data, numel);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+namespace ops = paddle::operators;
+REGISTER_OP_CUDA_KERNEL(trunc, ops::TruncCUDAKernel<float>,
+                        ops::TruncCUDAKernel<double>, ops::TruncCUDAKernel<int>,
+                        ops::TruncCUDAKernel<int64_t>);
+
+REGISTER_OP_CUDA_KERNEL(trunc_grad, ops::TruncCUDAGradKernel<float>,
+                        ops::TruncCUDAGradKernel<double>,
+                        ops::TruncCUDAGradKernel<int>,
+                        ops::TruncCUDAGradKernel<int64_t>);
diff --git a/paddle/fluid/operators/trunc_op.h b/paddle/fluid/operators/trunc_op.h
new file mode 100644
index 0000000000000..0f788eae5249c
--- /dev/null
+++ b/paddle/fluid/operators/trunc_op.h
@@ -0,0 +1,55 @@
+/* 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 <math.h>
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+
+namespace paddle {
+namespace operators {
+
+using Tensor = framework::Tensor;
+
+template <typename T>
+class TruncKernel : 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");
+
+    size_t numel = x->numel();
+    const T* x_data = x->data<T>();
+    T* out_data = out->mutable_data<T>(context.GetPlace());
+
+    for (size_t i = 0; i < numel; i++) {
+      out_data[i] = trunc(x_data[i]);
+    }
+  }
+};
+
+template <typename T>
+class TruncGradKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& context) const override {
+    auto* dx = context.Output<Tensor>(framework::GradVarName("X"));
+    T* dx_data = dx->mutable_data<T>(context.GetPlace());
+
+    int numel = dx->numel();
+    memset(dx_data, 0.0, numel * sizeof(T));
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
diff --git a/python/paddle/__init__.py b/python/paddle/__init__.py
index 738de4e393d77..b5315a5d19ac7 100755
--- a/python/paddle/__init__.py
+++ b/python/paddle/__init__.py
@@ -205,6 +205,7 @@
 from .tensor.math import prod  # noqa: F401
 from .tensor.math import broadcast_shape  # noqa: F401
 from .tensor.math import conj  # noqa: F401
+from .tensor.math import trunc  # noqa: F401
 from .tensor.math import digamma  # noqa: F401
 from .tensor.math import neg  # noqa: F401
 from .tensor.math import lgamma  # noqa: F401
@@ -490,6 +491,7 @@
            'log10',
            'concat',
            'check_shape',
+           'trunc'
            'digamma',
            'standard_normal'
 ]
diff --git a/python/paddle/fluid/tests/unittests/test_trunc_op.py b/python/paddle/fluid/tests/unittests/test_trunc_op.py
new file mode 100644
index 0000000000000..51844071138c7
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_trunc_op.py
@@ -0,0 +1,88 @@
+#   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.
+
+from __future__ import print_function
+
+import unittest
+import numpy as np
+from op_test import OpTest
+import paddle
+import paddle.fluid.core as core
+import paddle.fluid as fluid
+from paddle.fluid import Program, program_guard
+
+paddle.enable_static()
+
+
+class TestTruncOp(OpTest):
+    def setUp(self):
+        self.op_type = "trunc"
+        self.dtype = np.float64
+        np.random.seed(2021)
+        self.inputs = {'X': np.random.random((20, 20)).astype(self.dtype)}
+        self.outputs = {'Out': (np.trunc(self.inputs['X']))}
+
+    def init_dtype_type(self):
+        self.dtype = np.float64
+
+    def test_check_output(self):
+        self.check_output()
+
+    def test_check_grad(self):
+        self.check_grad(['X'], 'Out', numeric_grad_delta=1e-5)
+
+
+class TestFloatTruncOp(TestTruncOp):
+    def init_dtype_type(self):
+        self.dtype = np.float32
+
+
+class TestIntTruncOp(TestTruncOp):
+    def init_dtype_type(self):
+        self.dtype = np.int32
+
+
+class TestTruncAPI(unittest.TestCase):
+    def setUp(self):
+        self.shape = [20, 20]
+        self.x = np.random.random((20, 20)).astype(np.float32)
+        self.place = paddle.CPUPlace()
+
+    def test_api_static(self):
+        paddle.enable_static()
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.fluid.data('X', self.shape)
+            out = paddle.trunc(x)
+            exe = paddle.static.Executor(self.place)
+            res = exe.run(feed={'X': self.x}, fetch_list=[out])
+        out_ref = np.trunc(self.x)
+        for out in res:
+            self.assertEqual(np.allclose(out, out_ref, rtol=1e-08), True)
+
+    def test_api_dygraph(self):
+        paddle.disable_static(self.place)
+        x_tensor = paddle.to_tensor(self.x)
+        out = paddle.trunc(x_tensor)
+        out_ref = np.trunc(self.x)
+        self.assertEqual(np.allclose(out.numpy(), out_ref, rtol=1e-08), True)
+        paddle.enable_static()
+
+    def test_errors(self):
+        with paddle.static.program_guard(paddle.static.Program()):
+            x = paddle.fluid.data('X', [20, 20], 'bool')
+            self.assertRaises(TypeError, paddle.trunc, x)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/python/paddle/tensor/__init__.py b/python/paddle/tensor/__init__.py
index 8c83b1786b01e..206aa62adfb77 100755
--- a/python/paddle/tensor/__init__.py
+++ b/python/paddle/tensor/__init__.py
@@ -162,6 +162,7 @@
 from .math import any  # noqa: F401
 from .math import broadcast_shape  # noqa: F401
 from .math import conj  # noqa: F401
+from .math import trunc  # noqa: F401
 from .math import digamma  # noqa: F401
 from .math import neg  # noqa: F401
 from .math import lgamma  # noqa: F401
@@ -349,5 +350,6 @@
            'shape',
            'real',
            'imag',
+           'trunc'
            'digamma'
 ]
diff --git a/python/paddle/tensor/math.py b/python/paddle/tensor/math.py
index a9e24949aae2b..2ffb8d9302ccd 100755
--- a/python/paddle/tensor/math.py
+++ b/python/paddle/tensor/math.py
@@ -857,6 +857,50 @@ def add_n(inputs, name=None):
     return out
 
 
+def trunc(input, name=None):
+    '''
+    This API is used to returns a new tensor with the truncated integer values of input.
+    
+    Args:
+        input (Tensor): The input tensor, it's data type should be int32, int64, float32, float64.
+        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
+    
+    Returns:
+        Tensor: The output Tensor of trunc.
+    
+    Examples:
+        .. code-block:: python
+
+            import paddle
+
+            input = paddle.rand([2,2],'float32')
+            print(input)
+            # Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
+            #         [[0.02331470, 0.42374918],
+            #         [0.79647720, 0.74970269]])
+
+            output = paddle.trunc(input)
+            print(output)
+            # Tensor(shape=[2, 2], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
+            #         [[0., 0.],
+            #         [0., 0.]]))
+    '''
+    if in_dygraph_mode():
+        return core.ops.trunc(input)
+    else:
+        inputs = {"X": input}
+        attrs = {}
+
+        helper = LayerHelper("trunc", **locals())
+        check_variable_and_dtype(input, 'X', ['int32', 'int64', 'float32', 'float64'], 'trunc')
+        out = helper.create_variable_for_type_inference(dtype=input.dtype)
+
+        helper.append_op(
+            type="trunc", inputs=inputs, attrs=attrs, outputs={"Out": out})
+        return out
+
+
+
 def mm(input, mat2, name=None):
     """