diff --git a/paddle/fluid/API.spec b/paddle/fluid/API.spec
index d1742671a8b5da4e9e5ae82a99cd38f335e5145f..74a42ba5de91833885ec7a9ac5da06422c7b6603 100644
--- a/paddle/fluid/API.spec
+++ b/paddle/fluid/API.spec
@@ -47,6 +47,7 @@ paddle.fluid.ExecutionStrategy.__init__ __init__(self: paddle.fluid.core_avx.Par
 paddle.fluid.BuildStrategy.GradientScaleStrategy.__init__ __init__(self: paddle.fluid.core_avx.ParallelExecutor.BuildStrategy.GradientScaleStrategy, arg0: int) -> None
 paddle.fluid.BuildStrategy.ReduceStrategy.__init__ __init__(self: paddle.fluid.core_avx.ParallelExecutor.BuildStrategy.ReduceStrategy, arg0: int) -> None
 paddle.fluid.BuildStrategy.__init__ __init__(self: paddle.fluid.core_avx.ParallelExecutor.BuildStrategy) -> None
+paddle.fluid.gradients (ArgSpec(args=['targets', 'inputs', 'target_gradients', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None)), ('document', 'e2097e1e0ed84ae44951437bfe269a1b'))
 paddle.fluid.io.save_vars (ArgSpec(args=['executor', 'dirname', 'main_program', 'vars', 'predicate', 'filename'], varargs=None, keywords=None, defaults=(None, None, None, None)), ('document', '869104f47e6fd21d897c3fcc426aa942'))
 paddle.fluid.io.save_params (ArgSpec(args=['executor', 'dirname', 'main_program', 'filename'], varargs=None, keywords=None, defaults=(None, None)), ('document', '07ffd5351b30cf47172ccfd61bd0de6f'))
 paddle.fluid.io.save_persistables (ArgSpec(args=['executor', 'dirname', 'main_program', 'filename'], varargs=None, keywords=None, defaults=(None, None)), ('document', '9141bb5f32caf7975eb3fd88c8a1b2da'))
@@ -555,6 +556,7 @@ paddle.fluid.optimizer.PipelineOptimizer.find_section_opt (ArgSpec(args=['self',
 paddle.fluid.optimizer.PipelineOptimizer.minimize (ArgSpec(args=['self', 'loss', 'startup_program', 'parameter_list', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None, None)), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))
 paddle.fluid.optimizer.PipelineOptimizer.split_program (ArgSpec(args=['self', 'main_program', 'cut_list'], varargs=None, keywords=None, defaults=None), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))
 paddle.fluid.backward.append_backward (ArgSpec(args=['loss', 'parameter_list', 'no_grad_set', 'callbacks'], varargs=None, keywords=None, defaults=(None, None, None)), ('document', '08a5dd9f6f376ff3d55e0b1d92115cbd'))
+paddle.fluid.backward.gradients (ArgSpec(args=['targets', 'inputs', 'target_gradients', 'no_grad_set'], varargs=None, keywords=None, defaults=(None, None)), ('document', 'e2097e1e0ed84ae44951437bfe269a1b'))
 paddle.fluid.regularizer.L1DecayRegularizer.__init__ (ArgSpec(args=['self', 'regularization_coeff'], varargs=None, keywords=None, defaults=(0.0,)), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))
 paddle.fluid.regularizer.L2DecayRegularizer.__init__ (ArgSpec(args=['self', 'regularization_coeff'], varargs=None, keywords=None, defaults=(0.0,)), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))
 paddle.fluid.LoDTensor.__init__ 1. __init__(self: paddle.fluid.core_avx.LoDTensor, arg0: List[List[int]]) -> None  2. __init__(self: paddle.fluid.core_avx.LoDTensor) -> None
diff --git a/paddle/fluid/operators/activation_op.cc b/paddle/fluid/operators/activation_op.cc
index 8e38d5787bdadf4abd224386b3a9b03544a262e7..0c053cd0e54429ab20fc031425346d191d910e8c 100644
--- a/paddle/fluid/operators/activation_op.cc
+++ b/paddle/fluid/operators/activation_op.cc
@@ -604,21 +604,25 @@ class ActivationOpDoubleGrad : public framework::OperatorWithKernel {
 
   void InferShape(framework::InferShapeContext* ctx) const override {
     if (static_cast<int>(kDepValue) & static_cast<int>(kDepX)) {
-      if (ctx->HasOutput("DX")) {
+      // some op has no output DX, check HasOutputs("DX") here
+      if (HasOutputs("DX") && ctx->HasOutput("DX")) {
         ctx->ShareDim("X", "DX");
         ctx->ShareLoD("X", "DX");
       }
-      if (ctx->HasOutput("DDOut")) {
+      // some op has no output DDout, check HasOutputs("DDout") here
+      if (HasOutputs("DDOut") && ctx->HasOutput("DDOut")) {
         ctx->ShareDim("X", "DDOut");
         ctx->ShareLoD("X", "DDOut");
       }
     }
     if (static_cast<int>(kDepValue) & static_cast<int>(kDepOut)) {
-      if (ctx->HasOutput("DOut")) {
+      // some op has no output DOut, check HasOutputs("DOut") here
+      if (HasOutputs("DOut") && ctx->HasOutput("DOut")) {
         ctx->ShareDim("Out", "DOut");
         ctx->ShareLoD("Out", "DOut");
       }
-      if (ctx->HasOutput("DDOut")) {
+      // some op has no output DDOut, check HasOutputs("DDOut") here
+      if (HasOutputs("DDOut") && ctx->HasOutput("DDOut")) {
         ctx->ShareDim("Out", "DDOut");
         ctx->ShareLoD("Out", "DDOut");
       }
@@ -635,7 +639,6 @@ class ActivationOpDoubleGrad : public framework::OperatorWithKernel {
 //
 // ReluGrad: dx = dy if y >= 0 else 0
 // ReluGradGrad: ddy = ddx if y >= 0 else 0
-//               dy = 0
 //
 class ReluDoubleGradMaker : public ::paddle::framework::SingleGradOpDescMaker {
  public:
@@ -650,9 +653,7 @@ class ReluDoubleGradMaker : public ::paddle::framework::SingleGradOpDescMaker {
     // input2: ddx
     op->SetInput("DDX", OutputGrad(framework::GradVarName("X")));
     op->SetAttrMap(Attrs());
-    // output1: ddy
-    op->SetOutput("DOut", InputGrad("Out"));
-    // output2: ddy
+    // output: ddy
     op->SetOutput("DDOut", InputGrad(framework::GradVarName("Out")));
     return std::unique_ptr<::paddle::framework::OpDesc>(op);
   }
@@ -675,7 +676,6 @@ class LeakyReluDoubleGradMaker
     op->SetInput("DDX", OutputGrad(framework::GradVarName("X")));
     op->SetAttrMap(Attrs());
     // Out@GRAD@GRAD: ddy
-    op->SetOutput("DX", InputGrad("X"));
     op->SetOutput("DDOut", InputGrad(framework::GradVarName("Out")));
     return std::unique_ptr<::paddle::framework::OpDesc>(op);
   }
diff --git a/paddle/fluid/operators/activation_op.h b/paddle/fluid/operators/activation_op.h
index 5a4fb0828a7328d40490006f89a89581cf1fb3df..b516fc8a418599d429e47748f53e8a6ed1f65624 100644
--- a/paddle/fluid/operators/activation_op.h
+++ b/paddle/fluid/operators/activation_op.h
@@ -1321,10 +1321,6 @@ struct ReluGradGradFunctor : public BaseActivationFunctor<T> {
       auto ddout = framework::EigenVector<T>::Flatten(detail::Ref(ddOut));
       ddout.device(*d) = ddx * (out > static_cast<T>(0)).template cast<T>();
     }
-    if (dOut) {
-      auto dout = framework::EigenVector<T>::Flatten(detail::Ref(dOut));
-      dout.device(*d) = dout.constant(static_cast<T>(0));
-    }
   }
   static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
 };
@@ -1351,10 +1347,6 @@ struct LeakyReluGradGradFunctor : public BaseActivationFunctor<T> {
                               (x < static_cast<T>(0)).template cast<T>().eval())
                              .template cast<T>();
     }
-    if (dX) {
-      auto dx = framework::EigenVector<T>::Flatten(detail::Ref(dX));
-      dx.device(*d) = dx.constant(static_cast<T>(0));
-    }
   }
   static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
 };
diff --git a/paddle/fluid/operators/conv_op.cc b/paddle/fluid/operators/conv_op.cc
index 9572bb69e284b932a7dc791a778a91ed145ec51a..5c48a8ee8f56e8010a9263d8a2a460a1d22d420c 100644
--- a/paddle/fluid/operators/conv_op.cc
+++ b/paddle/fluid/operators/conv_op.cc
@@ -533,9 +533,16 @@ class Conv2DDoubleGradMaker : public framework::SingleGradOpDescMaker {
     // ddO, dI, dW
     // Unlike grad op, double grad op does not use name@GRAD@GRAD
     // as key of ops' inputs and outputs.
-    op->SetOutput("DDOutput", InputGrad(framework::GradVarName("Output")));
-    op->SetOutput("DFilter", InputGrad("Filter"));
-    op->SetOutput("DInput", InputGrad("Input"));
+    auto ddx = OutputGrad(framework::GradVarName("Input"));
+    auto ddw = OutputGrad(framework::GradVarName("Filter"));
+    std::vector<std::string> empty_str = {};
+
+    op->SetOutput(
+        "DDOutput",
+        ddx.empty() ? empty_str : InputGrad(framework::GradVarName("Output")));
+    op->SetOutput("DFilter", ddx.empty() ? empty_str : InputGrad("Filter"));
+    op->SetOutput("DInput", ddw.empty() ? empty_str : InputGrad("Input"));
+
     op->SetAttrMap(Attrs());
 
     return std::unique_ptr<framework::OpDesc>(op);
@@ -547,13 +554,13 @@ void ConvOpDoubleGrad::InferShape(framework::InferShapeContext* ctx) const {
   auto w_dims = ctx->GetInputDim("Filter");
   auto do_dims = ctx->GetInputDim("DOutput");
 
-  if (ctx->HasOutput("DDOutput")) {
+  if (ctx->HasOutput("DDOutput") && ctx->HasInput("DDInput")) {
     ctx->SetOutputDim("DDOutput", do_dims);
   }
-  if (ctx->HasOutput("DFilter")) {
+  if (ctx->HasOutput("DFilter") && ctx->HasInput("DDInput")) {
     ctx->SetOutputDim("DFilter", w_dims);
   }
-  if (ctx->HasOutput("DInput")) {
+  if (ctx->HasOutput("DInput") && ctx->HasInput("DDFilter")) {
     ctx->SetOutputDim("DInput", x_dims);
   }
 }
diff --git a/paddle/fluid/operators/mul_op.cc b/paddle/fluid/operators/mul_op.cc
index 6dac9041b6117df8e7b93378da42c2b0e224d558..bbf9fbfa1ff33d210417da750b9ab3813baf64e1 100644
--- a/paddle/fluid/operators/mul_op.cc
+++ b/paddle/fluid/operators/mul_op.cc
@@ -189,15 +189,15 @@ class MulDoubleGradOp : public framework::OperatorWithKernel {
     PADDLE_ENFORCE(ctx->HasInput("Y"), "Input(Y) should not be null");
     PADDLE_ENFORCE(ctx->HasInput("DOut"), "Input(DOut) should not be null");
 
-    if (ctx->HasOutput("DX")) {
+    if (ctx->HasOutput("DDOut") && ctx->HasInput("DDX")) {
+      ctx->ShareDim("DOut", "DDOut");
+    }
+    if (ctx->HasOutput("DX") && ctx->HasInput("DDY")) {
       ctx->ShareDim("X", "DX");
     }
-    if (ctx->HasOutput("DY")) {
+    if (ctx->HasOutput("DY") && ctx->HasInput("DDX")) {
       ctx->ShareDim("Y", "DY");
     }
-    if (ctx->HasOutput("DDOut")) {
-      ctx->ShareDim("DOut", "DDOut");
-    }
   }
 };
 
@@ -216,9 +216,15 @@ class MulDoubleGradMaker : public framework::SingleGradOpDescMaker {
     retv->SetInput("DDX", OutputGrad(framework::GradVarName("X")));
     retv->SetInput("DDY", OutputGrad(framework::GradVarName("Y")));
 
-    retv->SetOutput("DDOut", InputGrad(framework::GradVarName("Out")));
-    retv->SetOutput("DX", InputGrad("X"));
-    retv->SetOutput("DY", InputGrad("Y"));
+    auto ddx = OutputGrad(framework::GradVarName("X"));
+    auto ddw = OutputGrad(framework::GradVarName("Y"));
+    std::vector<std::string> empty_str = {};
+
+    retv->SetOutput("DDOut", (ddx.empty())
+                                 ? empty_str
+                                 : InputGrad(framework::GradVarName("Out")));
+    retv->SetOutput("DX", ddw.empty() ? empty_str : InputGrad("X"));
+    retv->SetOutput("DY", ddx.empty() ? empty_str : InputGrad("Y"));
 
     retv->SetAttrMap(Attrs());
     return retv;
diff --git a/paddle/fluid/operators/reduce_ops/reduce_mean_op.cc b/paddle/fluid/operators/reduce_ops/reduce_mean_op.cc
index 14593ea54ff24eca19d67939493987d8deabb261..d1b508792c255fc650459ebf308665551e1f8bde 100644
--- a/paddle/fluid/operators/reduce_ops/reduce_mean_op.cc
+++ b/paddle/fluid/operators/reduce_ops/reduce_mean_op.cc
@@ -46,17 +46,7 @@ class ReduceMeanDoubleGradMaker : public framework::GradOpDescMakerBase {
 
   std::vector<std::unique_ptr<framework::OpDesc>> operator()() const override {
     std::vector<std::unique_ptr<framework::OpDesc>> ops;
-    auto x_grads = InputGrad("X");
     auto x_gg = OutputGrad(framework::GradVarName("X"));  // input ddx
-    if (!x_grads.empty()) {
-      auto* x_grad_op = new framework::OpDesc();
-      x_grad_op->SetType("scale");
-      x_grad_op->SetInput("X", x_gg);
-      x_grad_op->SetOutput("Out", x_grads);
-      x_grad_op->SetAttr("scale", 0.0f);
-      ops.emplace_back(x_grad_op);
-    }
-
     auto out_grads = InputGrad(framework::GradVarName("Out"));
     if (!out_grads.empty()) {
       auto* out_grad_op = new framework::OpDesc();
diff --git a/paddle/fluid/operators/sum_op.cc b/paddle/fluid/operators/sum_op.cc
index 1eb4076d64d096f1fe230d7a7be211746135e847..e6c8772642573f1a4f331e8f33a77b34de7646fe 100644
--- a/paddle/fluid/operators/sum_op.cc
+++ b/paddle/fluid/operators/sum_op.cc
@@ -111,7 +111,7 @@ class SumOp : public framework::OperatorWithKernel {
                        "Input var[%s] should not be nullptr", x_vars_name[idx]);
         auto tensor =
             framework::GetLoDTensorOrSelectedRowsValueFromVar(*x_vars[idx]);
-        if (tensor->numel() == 0) {
+        if (tensor->numel() <= 0 || (!tensor->IsInitialized())) {
           continue;
         }
         if (dtype == -1) {
diff --git a/paddle/fluid/operators/sum_op.cu b/paddle/fluid/operators/sum_op.cu
index 5cecb7e09e7db2f3e4f63037352d3ee2b182ac3d..790626a59d0cd19ba0ccf463b1b270e629617078 100644
--- a/paddle/fluid/operators/sum_op.cu
+++ b/paddle/fluid/operators/sum_op.cu
@@ -126,12 +126,20 @@ void SumToLoDTensor(const framework::ExecutionContext &context) {
     auto &in_1 = in_vars[1]->Get<framework::LoDTensor>();
 
     auto length = in_0.numel();
-    if (length) {
+    if (length && in_0.IsInitialized() && in_1.IsInitialized()) {
       auto result = EigenVector<T>::Flatten(*out);
       auto &place = *dev_ctx.eigen_device();
       auto in_0_e = EigenVector<T>::Flatten(in_0);
       auto in_1_e = EigenVector<T>::Flatten(in_1);
       result.device(place) = in_0_e + in_1_e;
+    } else if (length && in_0.IsInitialized()) {
+      auto result = EigenVector<T>::Flatten(*out);
+      auto &place = *dev_ctx.eigen_device();
+      result.device(place) = EigenVector<T>::Flatten(in_0);
+    } else if (length && in_1.IsInitialized()) {
+      auto result = EigenVector<T>::Flatten(*out);
+      auto &place = *dev_ctx.eigen_device();
+      result.device(place) = EigenVector<T>::Flatten(in_1);
     }
     return;
   }
diff --git a/python/paddle/fluid/__init__.py b/python/paddle/fluid/__init__.py
index 70252a51e76388d88aab2277e3f6c90d8386d1e5..1a3a1dd5096381691d086849cb9f68f6641518ba 100644
--- a/python/paddle/fluid/__init__.py
+++ b/python/paddle/fluid/__init__.py
@@ -39,6 +39,7 @@ from . import contrib
 from . import nets
 from . import optimizer
 from . import backward
+from .backward import gradients
 from . import regularizer
 from . import average
 from . import metrics
@@ -72,7 +73,7 @@ Tensor = LoDTensor
 __all__ = framework.__all__ + executor.__all__ + \
     trainer_desc.__all__ + inferencer.__all__ + transpiler.__all__ + \
     parallel_executor.__all__ + lod_tensor.__all__ + \
-    data_feed_desc.__all__ + compiler.__all__ + [
+    data_feed_desc.__all__ + compiler.__all__ + backward.__all__ + [
         'io',
         'initializer',
         'layers',
diff --git a/python/paddle/fluid/backward.py b/python/paddle/fluid/backward.py
index 9030a33f3ef4531694481039330c48c0e7d22b4b..9de001849b9a875f215d2bd7bee5b9485b1d0d78 100644
--- a/python/paddle/fluid/backward.py
+++ b/python/paddle/fluid/backward.py
@@ -22,7 +22,7 @@ import six
 from .. import compat as cpt
 from . import unique_name
 
-__all__ = ['append_backward']
+__all__ = ['append_backward', 'gradients']
 
 
 def _rename_arg_(op_descs, old_name, new_name, begin_idx=None, end_idx=None):
@@ -142,6 +142,7 @@ def _addup_repetitive_outputs_(op_descs):
     pending_sum_ops = []
     var_rename_count = collections.defaultdict(int)
     renamed_vars = collections.defaultdict(list)
+    renamed_var_start_idx = collections.defaultdict(list)
     for idx, op_desc in enumerate(op_descs):
         for var_name in op_desc.input_arg_names():
             if len(renamed_vars[var_name]) > 1:
@@ -159,6 +160,7 @@ def _addup_repetitive_outputs_(op_descs):
                 if len(renamed_vars[var_name]) == 0:
                     # it's the first time we get the variable
                     renamed_vars[var_name] = [var_name]
+                    renamed_var_start_idx[var_name] = idx
                 else:
                     if len(renamed_vars[var_name]) == 1:
                         new_name = var_name + "@RENAME@" + \
@@ -166,7 +168,12 @@ def _addup_repetitive_outputs_(op_descs):
                         var_rename_count[var_name] += 1
                         # rename original var_name
                         renamed_vars[var_name][0] = new_name
-                        _rename_arg_(op_descs, var_name, new_name, 0, idx)
+                        # before change: _rename_arg_(op_descs, var_name,
+                        #                             new_name, 0, idx)
+                        # rename arg from idx of the first appearance
+                        # in backward, not always from 0
+                        _rename_arg_(op_descs, var_name, new_name,
+                                     renamed_var_start_idx[var_name], idx)
                         _rename_arg_(pending_sum_ops, var_name, new_name)
 
                         for p in op_desc.output_names()[:param_idx]:
@@ -254,7 +261,8 @@ def _append_backward_ops_(block,
                           target_block,
                           no_grad_dict,
                           grad_to_var,
-                          callbacks=None):
+                          callbacks=None,
+                          input_grad_names_set=None):
     """
     Create all grad ops, and insert them into given block
 
@@ -286,8 +294,13 @@ def _append_backward_ops_(block,
             sub_block = program.block(op._block_attr_id("sub_block"))
             grad_sub_block = program._create_block()
             grad_sub_block._set_forward_block_idx(sub_block.idx)
+            # see follwing comments for why set None here.
+            pre_input_grad_names_set = copy.copy(input_grad_names_set)
+            input_grad_names_set = None
             _append_backward_ops_(sub_block, sub_block.ops, grad_sub_block,
-                                  no_grad_dict, grad_to_var, callbacks)
+                                  no_grad_dict, grad_to_var, callbacks,
+                                  input_grad_names_set)
+            input_grad_names_set = pre_input_grad_names_set
 
             program._rollback()
             grad_sub_block_list.append(grad_sub_block.desc)
@@ -296,8 +309,33 @@ def _append_backward_ops_(block,
         grad_op_desc, op_grad_to_var = core.get_grad_op_desc(
             op.desc, cpt.to_text(no_grad_dict[block.idx]), grad_sub_block_list)
 
-        grad_op_descs.extend(grad_op_desc)
-        grad_to_var.update(op_grad_to_var)
+        # If input_grad_names_set is not None, extend grad_op_descs only when
+        # any input grad in outputs of previous grad ops.
+        # But this strategy is not suited for while op for some control flow,
+        # for example, for while op, the grads maybe generated in next loop.
+        if input_grad_names_set is not None:
+            is_append_grad = False
+            for op_desc in grad_op_desc:
+                input_grad_names = [
+                    name for name in op_desc.input_arg_names()
+                    if name.find(core.grad_var_suffix()) != -1
+                ]
+                # some code of gradient ops, like increment, are not very
+                # standard, there is no @GRAD in these ops' inputs.
+                if len(input_grad_names) == 0:
+                    is_append_grad = True
+                    break
+
+                if _some_in_set_(input_grad_names, input_grad_names_set):
+                    grad_op_descs.append(op_desc)
+                    is_append_grad = True
+                    for name in op_desc.output_arg_names():
+                        input_grad_names_set.add(name)
+            if is_append_grad:
+                grad_to_var.update(op_grad_to_var)
+        else:
+            grad_op_descs.extend(grad_op_desc)
+            grad_to_var.update(op_grad_to_var)
 
     grad_op_descs = _addup_repetitive_outputs_(grad_op_descs)
 
@@ -481,6 +519,8 @@ def append_backward(loss, parameter_list=None, no_grad_set=None,
         isinstance(callbacks, list)
 
     program = loss.block.program
+    program._appending_grad_times += 1
+
     if no_grad_set is None:
         no_grad_set = set()
     no_grad_set = copy.copy(no_grad_set)
@@ -511,10 +551,23 @@ def append_backward(loss, parameter_list=None, no_grad_set=None,
 
     block_no_grad_set = set(map(_strip_grad_suffix_, no_grad_dict[0]))
     op_path = _find_op_path_(root_block, [loss], [], block_no_grad_set)
+
     no_grad_dict[0].update(list(map(_append_grad_suffix_, block_no_grad_set)))
 
-    _append_backward_ops_(root_block, op_path, root_block, no_grad_dict,
-                          grad_to_var, callbacks)
+    input_grad_names_set = None
+    # For double backward, input_grad_names is used for filter
+    # some non-used gradients op.
+    if program._appending_grad_times > 1:
+        input_grad_names_set = set([_append_grad_suffix_(loss.name)])
+
+    _append_backward_ops_(
+        root_block,
+        op_path,
+        root_block,
+        no_grad_dict,
+        grad_to_var,
+        callbacks,
+        input_grad_names_set=input_grad_names_set)
 
     # Because calc_gradient may be called multiple times,
     # we need rename the internal gradient variables so that they have
@@ -618,17 +671,20 @@ def _find_op_path_(block, outputs, inputs, no_grad_set):
 
 def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
     """
-    Backpropagate the graidents of targets to inputs.
+    Backpropagate the gradients of targets to inputs.
 
     Args:
         targets(Variable|list[Variable]): The target variables
         inputs(Variable|list[Variable]): The input variables
+        target_gradients (Variable|list[Variable]|None): The gradient variables
+            of targets which has the same shape with targets, If None, ones will
+            be created for them.
         no_grad_set(set[string]): The names of variables that have no gradients
             in Block 0. All variables with `stop_gradient=True` from all blocks
             will be automatically added.
 
     Return:
-        (list[Variable]): list of gradients for inputs
+        (list[Variable]): A list of gradients for inputs
         If an input does not affect targets, the corresponding gradient variable
         will be None
     """
@@ -638,6 +694,8 @@ def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
 
     block = targets[0].block
     prog = block.program
+    # increase appending gradients times
+    prog._appending_grad_times += 1
     block_idx = block.idx
 
     if not target_gradients:
@@ -655,6 +713,8 @@ def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
 
     fwd_op_num = block.desc.op_size()
 
+    input_grad_names_set = set()
+
     target_grad_map = {}
     for i, grad in enumerate(target_gradients):
         target = targets[i]
@@ -670,6 +730,7 @@ def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
                                            'output_dim_idx': 0
                                        })
             block.desc.append_op().copy_from(op_desc)
+            input_grad_names_set.add(grad_name)
         else:
             if target.block.idx != block_idx or target.block.program != prog:
                 raise ValueError("all targets must be in the same block")
@@ -678,6 +739,12 @@ def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
                     "The shapes of target and grad are different: %s %s" % (
                         target.name, grad.name))
             target_grad_map[_append_grad_suffix_(target.name)] = grad.name
+            input_grad_names_set.add(grad.name)
+
+    # For double backward, input_grad_names is used for filter
+    # some non-used gradients op.
+    if prog._appending_grad_times == 1:
+        input_grad_names_set = None
 
     for input in inputs:
         if input.block.program != prog:
@@ -688,7 +755,13 @@ def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
     no_grad_dict[0].update(list(map(_append_grad_suffix_, block_no_grad_set)))
     grad_to_var = dict()
     grad_info_map = dict()
-    _append_backward_ops_(block, op_path, block, no_grad_dict, grad_to_var)
+    _append_backward_ops_(
+        block,
+        op_path,
+        block,
+        no_grad_dict,
+        grad_to_var,
+        input_grad_names_set=input_grad_names_set)
 
     # Because calc_gradient may be called multiple times,
     # we need rename the internal gradient variables so that they have
@@ -712,3 +785,40 @@ def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
         return grad_vars[0]
     else:
         return grad_vars
+
+
+def gradients(targets, inputs, target_gradients=None, no_grad_set=None):
+    """
+    Backpropagate the gradients of targets to inputs.
+
+    Args:
+        targets (Variable|list[Variable]): The target variables.
+        inputs (Variable|list[Variable]): The input variables.
+        target_gradients (Variable|list[Variable]|None): The gradient variables
+            of targets which has the same shape with targets, If None, ones will
+            be created for them.
+        no_grad_set (set[string]): The names of variables that have no gradients
+            in Block 0. All variables with `stop_gradient=True` from all blocks
+            will be automatically added.
+
+    Return:
+        (list[Variable]): A list of gradients for inputs
+        If an input does not affect targets, the corresponding gradient variable
+        will be None.
+
+    Examples:
+        .. code-block:: python
+
+            import paddle.fluid as fluid
+
+            x = fluid.layers.data(name='x', shape=[2,8,8], dtype='float32')
+            x.stop_gradient=False
+            y = fluid.layers.conv2d(x, 4, 1, bias_attr=False)
+            y = fluid.layers.relu(y)
+            y = fluid.layers.conv2d(y, 4, 1, bias_attr=False)
+            y = fluid.layers.relu(y)
+            z = fluid.gradients([y], x)
+            print(z)
+    """
+    outs = calc_gradient(targets, inputs, target_gradients, no_grad_set)
+    return _as_list(outs)
diff --git a/python/paddle/fluid/framework.py b/python/paddle/fluid/framework.py
index 1407c93a240b03514d576cb9505a9ff7b600b4f5..7e89c4a36ec4b6e5d33d779bb5fd54b4e2946ec7 100644
--- a/python/paddle/fluid/framework.py
+++ b/python/paddle/fluid/framework.py
@@ -2775,6 +2775,9 @@ class Program(object):
         # assigned if this program has been parsed by a pipeline optimizer
         self._pipeline_opt = None
 
+        # appending gradients times
+        self._appending_grad_times = 0
+
     @property
     def _is_mem_optimized(self):
         # if the program is optimized, operator input/outputs
@@ -3108,6 +3111,7 @@ class Program(object):
 
             p._current_role = self._current_role
             p.__op_role_var = self.__op_role_var
+            p._appending_grad_times = self._appending_grad_times
 
             p._sync_with_cpp()
 
diff --git a/python/paddle/fluid/tests/unittests/gradient_checker.py b/python/paddle/fluid/tests/unittests/gradient_checker.py
index 98ca93caeb6e75db5d5f54bbc4cfa4eac4635b17..3775f62097d277e4ae4331070c74933233298a6e 100644
--- a/python/paddle/fluid/tests/unittests/gradient_checker.py
+++ b/python/paddle/fluid/tests/unittests/gradient_checker.py
@@ -23,7 +23,6 @@ from itertools import product
 import paddle.fluid as fluid
 import paddle.fluid.core as core
 from paddle.fluid.executor import Executor
-from paddle.fluid.backward import calc_gradient
 from paddle.fluid.backward import _append_grad_suffix_, _as_list
 
 
@@ -183,7 +182,7 @@ def _compute_analytical_jacobian(program, x, y, place, scope):
     dy = program.global_block().create_var(
         name=dy_name, shape=y.shape, dtype=np_type, persistable=True)
     # append backward
-    dx = calc_gradient(y, x, dy)
+    dx = fluid.gradients(y, x, dy)
 
     # init dy tensor in scope
     value = np.zeros(y.shape, dtype=np_type)
@@ -382,7 +381,7 @@ def double_grad_check(x,
         ]
 
     # append first order grads
-    target_grads = calc_gradient(y, x, y_grads)
+    target_grads = fluid.gradients(y, x, y_grads)
 
     # y_grads are the input of first-order backward,
     # so, they are also the input of second-order backward.