diff --git a/paddle/phi/kernels/cpu/sgd_kernel.cc b/paddle/phi/kernels/cpu/sgd_kernel.cc
new file mode 100644
index 0000000000000000000000000000000000000000..91b39292612b52ee47fc2bc77c7f205158bdc29c
--- /dev/null
+++ b/paddle/phi/kernels/cpu/sgd_kernel.cc
@@ -0,0 +1,185 @@
+// Copyright (c) 2022 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/phi/kernels/sgd_kernel.h"
+#include "paddle/fluid/operators/jit/kernels.h"
+#include "paddle/phi/kernels/funcs/eigen/common.h"
+
+namespace phi {
+
+template <typename T>
+void sgd_dense_param_dense_grad_impl(const DenseTensor& param,
+                                     const DenseTensor& learning_rate,
+                                     const DenseTensor& grad,
+                                     DenseTensor* param_out) {
+  const auto sz = param_out->numel();
+  paddle::operators::jit::sgd_attr_t attr(1, sz, 1, sz, 1);
+  const T* lr = learning_rate.data<T>();
+  const T* param_data = param.data<T>();
+  const T* grad_data = grad.data<T>();
+  int64_t rows_idx = 0;
+  T* out_data = param_out->data<T>();
+
+  auto sgd =
+      paddle::operators::jit::KernelFuncs<paddle::operators::jit::SgdTuple<T>,
+                                          phi::CPUPlace>::Cache()
+          .At(attr);
+  sgd(lr, param_data, grad_data, &rows_idx, out_data, &attr);
+}
+
+template <>
+void sgd_dense_param_dense_grad_impl<phi::dtype::bfloat16>(
+    const DenseTensor& param,
+    const DenseTensor& learning_rate,
+    const DenseTensor& grad,
+    DenseTensor* param_out) {
+  auto p = EigenVector<phi::dtype::bfloat16>::Flatten(param);
+  auto g = EigenVector<phi::dtype::bfloat16>::Flatten(grad);
+  auto o = EigenVector<phi::dtype::bfloat16>::Flatten(*param_out);
+  const auto* lr = learning_rate.data<phi::dtype::bfloat16>();
+
+  o = p - lr[0] * g;
+}
+
+template <typename T>
+void sgd_dense_param_sparse_grad_impl(const DenseTensor& param,
+                                      const DenseTensor& learning_rate,
+                                      const SelectedRows& grad,
+                                      DenseTensor* param_out) {
+  const auto& grad_value = grad.value();
+  const auto& grad_rows = grad.rows();
+  const T* param_data = param.data<T>();
+  const T* grad_data = grad_value.data<T>();
+  const T* lr = learning_rate.data<T>();
+  const int64_t* rows_data = grad_rows.data();
+  T* out_data = param_out->data<T>();
+
+  paddle::operators::jit::sgd_attr_t attr;
+  attr.param_height = param_out->dims()[0];
+  attr.param_width = param_out->numel() / attr.param_height;
+  attr.grad_height = grad_rows.size();  // note: it is not grad->height()
+  attr.grad_width = grad_value.numel() / attr.grad_height;
+  attr.selected_rows_size = grad_rows.size();
+
+  auto sgd =
+      paddle::operators::jit::KernelFuncs<paddle::operators::jit::SgdTuple<T>,
+                                          phi::CPUPlace>::Cache()
+          .At(attr);
+  sgd(lr, param_data, grad_data, rows_data, out_data, &attr);
+}
+
+template <>
+void sgd_dense_param_sparse_grad_impl<phi::dtype::bfloat16>(
+    const DenseTensor& param,
+    const DenseTensor& learning_rate,
+    const SelectedRows& grad,
+    DenseTensor* param_out) {
+  const auto& grad_value = grad.value();
+  const auto& grad_rows = grad.rows();
+  const auto grad_height = grad.height();
+  const int64_t grad_val_height = static_cast<int64_t>(grad_rows.size());
+  const auto grad_width = grad_value.numel() / grad_val_height;
+
+  const auto* grad_data = grad_value.data<phi::dtype::bfloat16>();
+  auto* out_data = param_out->data<phi::dtype::bfloat16>();
+  const auto* lr = learning_rate.data<phi::dtype::bfloat16>();
+
+  for (size_t i = 0; i < grad_rows.size(); ++i) {
+    PADDLE_ENFORCE_LT(
+        grad_rows[i],
+        grad_height,
+        phi::errors::OutOfRange(
+            "Grad rows index value should be less than grad height."
+            "Got [%s], but expected less than [%s]",
+            grad_rows[i],
+            grad_height));
+    const int64_t row = grad_rows[i];
+    for (int64_t j = 0; j < grad_width; ++j) {
+      out_data[row * grad_width + j] -= lr[0] * grad_data[i * grad_width + j];
+    }
+  }
+}
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const DenseTensor& param,
+               const DenseTensor& learning_rate,
+               const DenseTensor& grad,
+               const DenseTensor& master_param,
+               bool multi_precision,
+               DenseTensor* param_out,
+               DenseTensor* master_param_out) {
+  dev_ctx.template Alloc<T>(param_out);
+  sgd_dense_param_dense_grad_impl<T>(param, learning_rate, grad, param_out);
+}
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const DenseTensor& param,
+               const DenseTensor& learning_rate,
+               const SelectedRows& grad,
+               const DenseTensor& master_param,
+               bool multi_precision,
+               DenseTensor* param_out,
+               DenseTensor* master_param_out) {
+  dev_ctx.template Alloc<T>(param_out);
+  sgd_dense_param_sparse_grad_impl<T>(param, learning_rate, grad, param_out);
+}
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const SelectedRows& param,
+               const DenseTensor& learning_rate,
+               const SelectedRows& grad,
+               const SelectedRows& master_param,
+               bool multi_precision,
+               SelectedRows* param_out,
+               SelectedRows* master_param_out) {
+  // for distributed training, a sparse var may be empty,
+  // just skip updating.
+  if (grad.rows().size() == 0) {
+    return;
+  }
+
+  auto param_row_width = param.value().dims()[1];
+  auto grad_row_width = grad.value().dims()[1];
+  PADDLE_ENFORCE_EQ(
+      param_row_width,
+      grad_row_width,
+      phi::errors::InvalidArgument(
+          "The param_row in SgdOP should have the same size with grad_row. "
+          "But received param_row's width is [%s], and grad_row's width is "
+          "[%s]",
+          param_row_width,
+          grad_row_width));
+
+  const auto* lr = learning_rate.data<T>();
+  const auto* grad_data = grad.value().data<T>();
+  auto* out_data = param_out->mutable_value()->data<T>();
+  for (size_t i = 0; i < grad.rows().size(); i++) {
+    int64_t id_index = param_out->AutoGrownIndex(grad.rows()[i], false);
+    PADDLE_ENFORCE_GE(
+        id_index,
+        static_cast<int64_t>(0),
+        phi::errors::InvalidArgument(
+            "The id in SgdOp should be >= 0. But recevied id_index is [%s]",
+            id_index));
+    for (int64_t j = 0; j < grad_row_width; j++) {
+      out_data[id_index * grad_row_width + j] -=
+          lr[0] * grad_data[i * grad_row_width + j];
+    }
+  }
+}
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/gpu/sgd_kernel.cu b/paddle/phi/kernels/gpu/sgd_kernel.cu
new file mode 100644
index 0000000000000000000000000000000000000000..076bd0a7ad1e4ac1a70907823f7b23fb8bc620da
--- /dev/null
+++ b/paddle/phi/kernels/gpu/sgd_kernel.cu
@@ -0,0 +1,167 @@
+// Copyright (c) 2022 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/phi/kernels/sgd_kernel.h"
+
+#include "paddle/fluid/operators/amp/fp16_type_traits.h"
+#include "paddle/fluid/platform/device/gpu/gpu_primitives.h"
+#include "paddle/phi/backends/gpu/gpu_helper.h"
+
+namespace phi {
+
+template <typename T, typename MT>
+__global__ void SGDKernelMT(const T* param,
+                            const T* grad,
+                            const T* learning_rate,
+                            const int num,
+                            T* param_out,
+                            const MT* master_param,
+                            MT* master_param_out) {
+  MT lr = static_cast<MT>(learning_rate[0]);
+  CUDA_KERNEL_LOOP(i, num) {
+    MT p_data = master_param ? master_param[i] : static_cast<MT>(param[i]);
+    MT g_data = static_cast<MT>(grad[i]);
+    p_data = p_data - lr * g_data;
+    param_out[i] = static_cast<T>(p_data);
+    if (master_param_out) {
+      master_param_out[i] = p_data;
+    }
+  }
+}
+
+template <typename T>
+__global__ void SparseSGDFunctorKernel(const T* selected_rows,
+                                       const int64_t* rows,
+                                       const T* learning_rate,
+                                       T* tensor_out,
+                                       int64_t row_numel,
+                                       int64_t limit) {
+  for (int64_t i = blockIdx.x; i < limit; i += gridDim.x) {
+    const T* selected_rows_ptr = selected_rows + i * row_numel;
+    T* tensor_out_ptr = tensor_out + rows[i] * row_numel;
+    for (int64_t index = threadIdx.x; index < row_numel; index += blockDim.x) {
+      // Since index in rows of SelectedRows can be duplicate, we have to use
+      // Atomic Operation to avoid concurrent write error.
+      paddle::platform::CudaAtomicAdd(
+          tensor_out_ptr + index,
+          -static_cast<T>(1.0) * learning_rate[0] * selected_rows_ptr[index]);
+    }
+  }
+}
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const DenseTensor& param,
+               const DenseTensor& learning_rate,
+               const DenseTensor& grad,
+               const DenseTensor& master_param,
+               bool multi_precision,
+               DenseTensor* param_out,
+               DenseTensor* master_param_out) {
+  using MPDType = typename paddle::operators::details::MPTypeTrait<T>::Type;
+  // do check here
+  // if (multi_precision) {
+  //   bool has_master =
+  //       ctx.HasInput("MasterParam") && ctx.HasOutput("MasterParamOut");
+
+  // }
+  const MPDType* master_in_data =
+      multi_precision ? master_param.data<MPDType>() : nullptr;
+  MPDType* master_out_data =
+      multi_precision
+          ? master_param_out->mutable_data<MPDType>(dev_ctx.GetPlace())
+          : nullptr;
+
+  int block = 512;
+  int grid = (param.numel() + block - 1) / block;
+
+  SGDKernelMT<T, MPDType><<<grid, block, 0, dev_ctx.stream()>>>(
+      param.data<T>(),
+      grad.data<T>(),
+      learning_rate.data<T>(),
+      param.numel(),
+      param_out->mutable_data<T>(ctx.GetPlace()),
+      master_in_data,
+      master_out_data);
+}
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const DenseTensor& param,
+               const DenseTensor& learning_rate,
+               const SelectedRows& grad,
+               const DenseTensor& master_param,
+               bool multi_precision,
+               DenseTensor* param_out,
+               DenseTensor* master_param_out) {
+  using MPDType = typename paddle::operators::details::MPTypeTrait<T>::Type;
+  // do some check here
+  // if (multi_precision) {
+  //   bool has_master =
+  //       ctx.HasInput("MasterParam") && ctx.HasOutput("MasterParamOut");
+
+  // }
+  const MPDType* master_in_data =
+      multi_precision ? master_param.data<MPDType>() : nullptr;
+  MPDType* master_out_data =
+      multi_precision
+          ? master_param_out->mutable_data<MPDType>(dev_ctx.GetPlace())
+          : nullptr;
+
+  PADDLE_ENFORCE_EQ(
+      &param,
+      param_out,
+      phi::errors::InvalidArgument(
+          "The input tensor Param of SgdOp should be equal with ParamOut "
+          "if variable's type is SelectedRows."));
+
+  auto in_height = grad.height();
+  auto out_dims = param_out->dims();
+  PADDLE_ENFORCE_EQ(in_height,
+                    out_dims[0],
+                    phi::errors::InvalidArgument(
+                        "The input tensor Grad's height of SgdOp should be "
+                        "equal with ParamOut's dims. But received Grad's "
+                        "height [%s] and ParamOut's dims [%s]",
+                        in_height,
+                        out_dims[0]));
+
+  auto& in_value = grad.value();
+  auto& in_rows = grad.rows();
+
+  int64_t in_row_numel = in_value.numel() / in_rows.size();
+  PADDLE_ENFORCE_EQ(in_row_numel,
+                    param_out->numel() / in_height,
+                    phi::errors::InvalidArgument(
+                        "The in_row_numel of SgdOp should be equal with "
+                        "param_out's numel / in_height."));
+
+  auto* in_data = in_value.data<T>();
+  auto* out_data = param_out->data<T>();
+
+  const int kThreadsPerBlock = 256;
+  int thread_x = kThreadsPerBlock;
+  int max_threads = dev_ctx.GetMaxPhysicalThreadCount();
+  int max_blocks = std::max(max_threads / kThreadsPerBlock, 1);
+  paddle::framework::MixVector<int64_t> mixv_in_rows(&in_rows);
+  SparseSGDFunctorKernel<<<max_blocks, thread_x, 0, dev_ctx..stream()>>>(
+      in_data,
+      mixv_in_rows.CUDAData(dev_ctx.GetPlace()),
+      learning_rate.data<T>(),
+      out_data,
+      in_row_numel,
+      in_rows.size());
+}
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/sgd_kernel.h b/paddle/phi/kernels/sgd_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..9490940325e91efddc861561ab9e5d233c34eed2
--- /dev/null
+++ b/paddle/phi/kernels/sgd_kernel.h
@@ -0,0 +1,52 @@
+// Copyright (c) 2022 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 "paddle/phi/core/dense_tensor.h"
+#include "paddle/phi/core/selected_rows.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const DenseTensor& param,
+               const DenseTensor& learning_rate,
+               const DenseTensor& grad,
+               const DenseTensor& master_param,
+               bool multi_precision,
+               DenseTensor* param_out,
+               DenseTensor* master_param_out);
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const DenseTensor& param,
+               const DenseTensor& learning_rate,
+               const SelectedRows& grad,
+               const DenseTensor& master_param,
+               bool multi_precision,
+               DenseTensor* param_out,
+               DenseTensor* master_param_out);
+
+template <typename T, typename Context>
+void SGDKernel(const Context& dev_ctx,
+               const SelectedRows& param,
+               const DenseTensor& learning_rate,
+               const SelectedRows& grad,
+               const SelectedRows& master_param,
+               bool multi_precision,
+               SelectedRows* param_out,
+               SelectedRows* master_param_out);
+
+}  // namespace phi