diff --git a/paddle/framework/backward.cc b/paddle/framework/backward.cc
index 1a24d266db14bf142e3227a2ace0daa5126224cb..b6c46302b1f39b79f60e6f6accb4a3e6becb001f 100644
--- a/paddle/framework/backward.cc
+++ b/paddle/framework/backward.cc
@@ -79,11 +79,11 @@ static std::shared_ptr<OperatorBase> BackwardImpl(
     std::unordered_map<std::string /*var name*/,
                        std::vector<size_t> /*op offset*/>
         dup_output_ops;
-    size_t local_op_id = 0;
     // Because it is a net op, it can static_cast.
     auto& forwardNet = static_cast<const NetOp&>(forwardOp);
 
     // travesal subnet/op
+    size_t local_op_id = 0;
     for (auto it = forwardNet.ops_.rbegin(); it != forwardNet.ops_.rend();
          ++it) {
       auto fwd = *it;
diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index 7472a970b916b498491e1f5809d8d84b896cee01..cb1d402526e0b0008263c8f19e4d175c6e1502f6 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -149,7 +149,6 @@ TEST(Backward, simple_op_grad) {
   auto fwd = f::OpRegistry::CreateOp("rowwise_add", {"X", "b"}, {"Out"}, {});
   ASSERT_NE(fwd, nullptr);
   auto gop = f::OpRegistry::CreateGradOp(*fwd);
-  LOG(INFO) << gop->DebugString();
   ASSERT_EQ(1UL, gop->inputs_.size());
   ASSERT_EQ("Out" + f::OperatorBase::GRAD_VAR_SUFFIX(), gop->inputs_[0]);
   ASSERT_EQ("rowwise_add_grad", gop->type_);
@@ -161,18 +160,19 @@ TEST(Backward, simple_op_grad) {
   //  LOG(INFO) << gop->Output("X" + "@GRAD");
 }
 
-TEST(Backward, simple_net_grad) {
-  auto fwd = f::OpRegistry::CreateOp("rowwise_add", {"X", "b"}, {"Out"}, {});
+TEST(Backward, simple_op_not_need_grad) {
+  auto fwd = f::OpRegistry::CreateOp("rowwise_add", {"x", "b"}, {"out"}, {});
   ASSERT_NE(fwd, nullptr);
-  auto gop = f::Backward(*fwd, {});
+  auto gop = f::Backward(*fwd, {"x"});
   LOG(INFO) << gop->DebugString();
+  ASSERT_NE(gop->outputs_.find("x" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+            gop->outputs_.end());
 }
 
 TEST(Backward, net_fc_backward_normal) {
   std::shared_ptr<f::OperatorBase> fwd = f::OpRegistry::CreateOp(
       "fc", {"X", "w", "b"}, {"mul_result", "add_result", "out"}, {});
   ASSERT_NE(fwd, nullptr);
-  LOG(INFO) << fwd->DebugString();
   std::shared_ptr<f::OperatorBase> gop = f::Backward(*fwd, {});
   ASSERT_TRUE(gop->IsNetOp());
   auto net = static_cast<f::NetOp *>(gop.get());