diff --git a/paddle/fluid/operators/randperm_op.cc b/paddle/fluid/operators/randperm_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..67d7c578dcd777d084fcbe14658a9ae2cd3e0ed6
--- /dev/null
+++ b/paddle/fluid/operators/randperm_op.cc
@@ -0,0 +1,96 @@
+/* Copyright (c) 2020 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/randperm_op.h"
+#include <string>
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+
+namespace paddle {
+namespace operators {
+
+class RandpermOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+  void InferShape(framework::InferShapeContext *ctx) const override {
+    PADDLE_ENFORCE_EQ(ctx->HasOutput("Out"), true,
+                      platform::errors::NotFound(
+                          "The output(Out) of randperm op must not be null."));
+    int n = ctx->Attrs().Get<int>("n");
+    PADDLE_ENFORCE_GT(
+        n, 0, platform::errors::InvalidArgument(
+                  "The input(n) of randperm op must be greater than 0."));
+
+    ctx->SetOutputDim("Out", framework::make_ddim({n}));
+  }
+
+ protected:
+  framework::OpKernelType GetExpectedKernelType(
+      const framework::ExecutionContext &ctx) const override {
+    auto data_type =
+        static_cast<framework::proto::VarType::Type>(ctx.Attr<int>("dtype"));
+    return framework::OpKernelType(data_type, ctx.GetPlace());
+  }
+};
+
+class RandpermOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddOutput("Out", "The output tensor of randperm op.");
+
+    AddAttr<int>(
+        "n", "The upper bound (exclusive), and it should be greater than 0.");
+    AddAttr<int>("dtype",
+                 "The data type of output tensor. "
+                 "Default: 3[int64].")
+        .SetDefault(framework::proto::VarType::INT64);
+    AddAttr<int>("seed",
+                 "Random seed used for permute samples. "
+                 "0 means use a seed generated by the system."
+                 "Note that if seed is not 0, this operator will always "
+                 "generate the same random permutation every time. "
+                 "Default: 0.")
+        .SetDefault(0);
+
+    AddComment(R"DOC( 
+This operator returns a random permutation of integers from 0 to n-1.
+)DOC");
+  }
+};
+
+class RandpermOpVarTypeInference : public framework::VarTypeInference {
+ public:
+  void operator()(framework::InferVarTypeContext *ctx) const override {
+    auto var_data_type = static_cast<framework::proto::VarType::Type>(
+        boost::get<int>(ctx->GetAttr("dtype")));
+    auto out_var_name = ctx->Output("Out").front();
+    ctx->SetDataType(out_var_name, var_data_type);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+REGISTER_OPERATOR(
+    randperm, paddle::operators::RandpermOp, paddle::operators::RandpermOpMaker,
+    paddle::framework::EmptyGradOpMaker<paddle::framework::OpDesc>,
+    paddle::framework::EmptyGradOpMaker<paddle::imperative::OpBase>,
+    paddle::operators::RandpermOpVarTypeInference);
+
+template <typename T>
+using kernel =
+    paddle::operators::RandpermKernel<paddle::platform::CPUDeviceContext, T>;
+
+REGISTER_OP_CPU_KERNEL(randperm, kernel<int64_t>, kernel<int>);
diff --git a/paddle/fluid/operators/randperm_op.cu b/paddle/fluid/operators/randperm_op.cu
new file mode 100644
index 0000000000000000000000000000000000000000..21ae1a4968a7e1fd9fd8aee3a12ea71c42a74d46
--- /dev/null
+++ b/paddle/fluid/operators/randperm_op.cu
@@ -0,0 +1,23 @@
+/* Copyright (c) 2020 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/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+#include "paddle/fluid/operators/randperm_op.h"
+
+template <typename T>
+using kernel =
+    paddle::operators::RandpermKernel<paddle::platform::CUDADeviceContext, T>;
+
+REGISTER_OP_CUDA_KERNEL(randperm, kernel<int64_t>, kernel<int>);
diff --git a/paddle/fluid/operators/randperm_op.h b/paddle/fluid/operators/randperm_op.h
new file mode 100644
index 0000000000000000000000000000000000000000..64ef1c771423f2d820c73df8ed9ff25834f07875
--- /dev/null
+++ b/paddle/fluid/operators/randperm_op.h
@@ -0,0 +1,65 @@
+/* Copyright (c) 2020 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 <algorithm>
+#include <cstdlib>
+#include <ctime>
+#include <string>
+#include <vector>
+#include "paddle/fluid/framework/operator.h"
+#include "paddle/fluid/framework/tensor_util.h"
+#include "paddle/fluid/platform/place.h"
+
+namespace paddle {
+namespace operators {
+
+template <typename T>
+static inline void random_permate(T* data_ptr, int num, unsigned int seed) {
+  for (int i = 0; i < num; ++i) {
+    data_ptr[i] = static_cast<T>(i);
+  }
+  if (seed == 0) {
+    seed = std::random_device()();
+  }
+  std::srand(seed);
+  std::random_shuffle(data_ptr, data_ptr + num);
+}
+
+template <typename DeviceContext, typename T>
+class RandpermKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& ctx) const override {
+    int n = ctx.Attr<int>("n");
+    unsigned int seed = static_cast<unsigned int>(ctx.Attr<int>("seed"));
+    framework::Variable* out_var = ctx.OutputVar("Out");
+    framework::Tensor* out_tensor =
+        framework::GetMutableLoDTensorOrSelectedRowsValueFromVar(out_var);
+
+    if (platform::is_cpu_place(ctx.GetPlace())) {
+      T* out_data = out_tensor->mutable_data<T>(platform::CPUPlace());
+      random_permate<T>(out_data, n, seed);
+    } else {
+      framework::Tensor tmp_tensor;
+      tmp_tensor.Resize(framework::make_ddim({n}));
+      T* tmp_data = tmp_tensor.mutable_data<T>(platform::CPUPlace());
+      random_permate<T>(tmp_data, n, seed);
+      framework::TensorCopy(tmp_tensor, platform::CUDAPlace(), out_tensor);
+    }
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
diff --git a/python/paddle/__init__.py b/python/paddle/__init__.py
index 2b13bab747995d303b0619e6e86242ee3a048e5d..c9606f6fb4fd4ca4cacd86881860bb50d942ab21 100644
--- a/python/paddle/__init__.py
+++ b/python/paddle/__init__.py
@@ -87,7 +87,7 @@ from .tensor.logic import elementwise_equal  #DEFINE_ALIAS
 # from .tensor.random import uniform   #DEFINE_ALIAS
 # from .tensor.random import shuffle   #DEFINE_ALIAS
 # from .tensor.random import randn   #DEFINE_ALIAS
-# from .tensor.random import randperm   #DEFINE_ALIAS
+from .tensor.random import randperm
 # from .tensor.random import rand   #DEFINE_ALIAS
 # from .tensor.random import randint   #DEFINE_ALIAS
 # from .tensor.math import abs   #DEFINE_ALIAS
diff --git a/python/paddle/fluid/tests/unittests/test_randperm_op.py b/python/paddle/fluid/tests/unittests/test_randperm_op.py
new file mode 100644
index 0000000000000000000000000000000000000000..2fbdc83f3abffb7f832e0b0396b745635cc47a00
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_randperm_op.py
@@ -0,0 +1,175 @@
+#   Copyright (c) 2020 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 numpy as np
+from op_test import OpTest
+import paddle
+import paddle.fluid as fluid
+import paddle.fluid.core as core
+from paddle.fluid.op import Operator
+from paddle.fluid import Program, program_guard
+
+
+def check_randperm_out(n, data_np):
+    assert isinstance(data_np, np.ndarray), \
+        "The input data_np should be np.ndarray."
+    gt_sorted = np.arange(n)
+    out_sorted = np.sort(data_np)
+    return list(gt_sorted == out_sorted)
+
+
+def error_msg(data_np):
+    return "The sorted ground truth and sorted out should " + \
+ "be equal, out = " + str(data_np)
+
+
+def convert_dtype(dtype_str):
+    dtype_str_list = ["int32", "int64"]
+    dtype_num_list = [2, 3]
+    assert dtype_str in dtype_str_list, dtype_str + \
+        " should in " + str(dtype_str_list)
+    return dtype_num_list[dtype_str_list.index(dtype_str)]
+
+
+class TestRandpermOp(OpTest):
+    """ Test randperm op."""
+
+    def setUp(self):
+        self.op_type = "randperm"
+        self.n = 200
+        self.dtype = "int64"
+        self.device = None
+        self.seed = 0
+
+        self.inputs = {}
+        self.outputs = {"Out": np.zeros((self.n)).astype(self.dtype)}
+        self.init_attrs()
+        self.attrs = {
+            "n": self.n,
+            "dtype": convert_dtype(self.dtype),
+            "device": self.device,
+            "seed": self.seed,
+        }
+
+    def init_attrs(self):
+        pass
+
+    def test_check_output(self):
+        self.check_output_customized(self.verify_output)
+
+    def verify_output(self, outs):
+        out_np = np.array(outs[0])
+        self.assertTrue(
+            check_randperm_out(self.n, out_np), msg=error_msg(out_np))
+
+
+class TestRandpermOp_attr_n(TestRandpermOp):
+    """ Test randperm op for attr n. """
+
+    def init_attrs(self):
+        self.n = 10000
+
+
+class TestRandpermOp_attr_int32(TestRandpermOp):
+    """ Test randperm op for attr int32 dtype. """
+
+    def init_attrs(self):
+        self.dtype = "int32"
+
+
+class TestRandpermOp_attr_device_cpu(TestRandpermOp):
+    """ Test randperm op for cpu device. """
+
+    def init_attrs(self):
+        self.device = "cpu"
+
+
+class TestRandpermOp_attr_device_gpu(TestRandpermOp):
+    """ Test randperm op for gpu device. """
+
+    def init_attrs(self):
+        self.device = "gpu"
+
+
+class TestRandpermOp_attr_seed(TestRandpermOp):
+    """ Test randperm op for attr seed. """
+
+    def init_attrs(self):
+        self.seed = 10
+
+
+class TestRandpermOpError(unittest.TestCase):
+    """ Test randperm op for raise error. """
+
+    def test_errors(self):
+        main_prog = Program()
+        start_prog = Program()
+        with program_guard(main_prog, start_prog):
+
+            def test_Variable():
+                out = np.arange(10)
+                paddle.randperm(n=10, out=out)
+
+            self.assertRaises(TypeError, test_Variable)
+
+            def test_value():
+                paddle.randperm(n=-3)
+
+            self.assertRaises(ValueError, test_value)
+
+
+class TestRandpermOp_attr_out(unittest.TestCase):
+    """ Test randperm op for attr out. """
+
+    def test_attr_tensor_API(self):
+        startup_program = fluid.Program()
+        train_program = fluid.Program()
+        with fluid.program_guard(train_program, startup_program):
+            n = 10
+            data_1 = fluid.layers.fill_constant([n], "int64", 3)
+            paddle.randperm(n=n, out=data_1)
+
+            data_2 = paddle.randperm(n=n, dtype="int32", device="cpu")
+
+            place = fluid.CPUPlace()
+            if fluid.core.is_compiled_with_cuda():
+                place = fluid.CUDAPlace(0)
+            exe = fluid.Executor(place)
+
+            exe.run(startup_program)
+            outs = exe.run(train_program, fetch_list=[data_1, data_2])
+
+            out_np = np.array(outs[0])
+            self.assertTrue(
+                check_randperm_out(n, out_np), msg=error_msg(out_np))
+
+
+class TestRandpermDygraphMode(unittest.TestCase):
+    def test_check_output(self):
+        with fluid.dygraph.guard():
+            n = 10
+            data_1 = paddle.randperm(n, dtype="int64")
+            data_1_np = data_1.numpy()
+            self.assertTrue(
+                check_randperm_out(n, data_1_np), msg=error_msg(data_1_np))
+
+            data_2 = paddle.randperm(n, dtype="int32", device="cpu")
+            data_2_np = data_2.numpy()
+            self.assertTrue(
+                check_randperm_out(n, data_2_np), msg=error_msg(data_2_np))
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/python/paddle/tensor/__init__.py b/python/paddle/tensor/__init__.py
index 2923f2bf1c6f2703d86b408694568b329fa7cf04..68b487107c325f88c1c01456f93c1a3ad96e1019 100644
--- a/python/paddle/tensor/__init__.py
+++ b/python/paddle/tensor/__init__.py
@@ -63,9 +63,9 @@ from .logic import elementwise_equal  #DEFINE_ALIAS
 # from .random import uniform   #DEFINE_ALIAS
 # from .random import shuffle   #DEFINE_ALIAS
 # from .random import randn   #DEFINE_ALIAS
-# from .random import randperm   #DEFINE_ALIAS
 # from .random import rand   #DEFINE_ALIAS
 # from .random import randint   #DEFINE_ALIAS
+from .random import randperm
 # from .math import abs   #DEFINE_ALIAS
 # from .math import acos   #DEFINE_ALIAS
 # from .math import asin   #DEFINE_ALIAS
diff --git a/python/paddle/tensor/random.py b/python/paddle/tensor/random.py
index 6f8ff58d651bec5356c09d60a78d8a7deac44208..97fd319e7db514300914a8536a64052a4aa63ec8 100644
--- a/python/paddle/tensor/random.py
+++ b/python/paddle/tensor/random.py
@@ -17,6 +17,100 @@
 #            'uniform', 
 #            'shuffle',
 #            'randn',
-#            'randperm',
 #            'rand',
 #            'randint']
+
+from ..fluid import core
+from ..fluid.framework import device_guard, in_dygraph_mode, _varbase_creator
+from ..fluid.layers.layer_function_generator import templatedoc
+from ..fluid.layer_helper import LayerHelper
+from ..fluid.data_feeder import convert_dtype, check_variable_and_dtype, check_type, check_dtype
+
+__all__ = ['randperm']
+
+
+@templatedoc()
+def randperm(n,
+             out=None,
+             dtype="int64",
+             device=None,
+             stop_gradient=True,
+             seed=0):
+    """
+    ${comment}
+
+    Args:
+        n (int): The upper bound (exclusive), and it should be greater than 0.
+        out (Variable, optional): Optional output which can be any created 
+            Variable that meets the requirements to store the result of operation.
+            If out is None, a new Varibale will be create to store the result. 
+            Default: None.
+        dtype (np.dtype|core.VarDesc.VarType|str, optional): The type of the 
+            output Tensor. Supported data types: int64, int32. Default: int32.
+        device (str, optional): Specific the output variable to be saved in cpu
+            or gpu memory. Supported None, 'cpu', 'gpu'. If it is None, the output
+            variable will be automatically assigned devices.
+            Default: None.
+        stop_gradient (bool, optional): Whether grad should record operations 
+            on the returned tensor. Default: True.
+        seed (int, optional): Random seed used for permute samples. If seed is 
+            equal to 0, it means use a seed generated by the system. Note that 
+            if seed is not 0, this operator will always generate the same random 
+            permutation every time. Default: 0.
+
+    Returns:
+        ${out_comment}.
+
+    Return Type:
+        ${out_type}
+
+    Examples:
+        .. code-block:: python
+
+	    import paddle
+	    import paddle.fluid as fluid
+
+	    num = 6
+	    is_use_gpu = False
+
+	    data_1 = paddle.randperm(num)
+	    fluid.layers.Print(data_1)
+
+	    data_2 = paddle.randperm(num, dtype="int32", seed=1)
+	    fluid.layers.Print(data_2)
+
+	    data_3 = paddle.randperm(num, stop_gradient=False, device="cpu")
+	    fluid.layers.Print(data_3)
+
+	    paddle.randperm(num, out=data_3)
+	    fluid.layers.Print(data_3)
+
+	    place = fluid.CUDAPlace(0) if is_use_gpu else fluid.CPUPlace()
+	    exe = fluid.Executor(place)
+	    exe.run(fluid.default_startup_program())
+	    exe.run()
+ 
+    """
+
+    if n < 1:
+        raise ValueError("The input n should be greater than 0 in randperm op.")
+    check_dtype(dtype, 'dtype', ['int64', 'int32'], 'randperm')
+    dtype = convert_dtype(dtype)
+    if device not in [None, 'cpu', 'gpu']:
+        raise ValueError("The input device should in [None, 'cpu', 'gpu'].")
+    check_type(stop_gradient, 'stop_gradient', bool, 'randperm')
+
+    helper = LayerHelper("randperm", **locals())
+    if out is None:
+        out = helper.create_variable_for_type_inference(dtype=dtype)
+    else:
+        check_variable_and_dtype(out, 'out', [dtype], 'randperm')
+    if stop_gradient:
+        out.stop_gradient = True
+    inputs = dict()
+    outputs = {'Out': [out]}
+    attrs = {'n': n, 'dtype': out.dtype, 'seed': seed}
+    with device_guard(device):
+        helper.append_op(
+            type='randperm', inputs=inputs, outputs=outputs, attrs=attrs)
+    return out