diff --git a/paddle/framework/backward_test.cc b/paddle/framework/backward_test.cc
index 69faee9fb71516c8a13a75b493dc193669623800..9886679d309b74a23a3f4e85e70a7ceec32c3ca8 100644
--- a/paddle/framework/backward_test.cc
+++ b/paddle/framework/backward_test.cc
@@ -167,15 +167,28 @@ TEST(Backward, simple_op_not_need_grad) {
   auto gop = f::Backward(*fwd, {"X"});
   LOG(INFO) << "full " << gop->DebugString();
   ASSERT_NE(std::find(gop->outputs_.begin(), gop->outputs_.end(),
-                      "X" + f::OperatorBase::GRAD_VAR_SUFFIX()),
+                      std::string("X") + f::OperatorBase::GRAD_VAR_SUFFIX()),
             gop->outputs_.end());
+
   auto no_input_gop = f::Backward(*fwd, {"X", "b"});
-  LOG(INFO) << "no input gop " << no_input_gop->DebugString();
+  LOG(INFO) << "no input gop " << gop->DebugString();
   ASSERT_NE(no_input_gop, nullptr);
-  ASSERT_EQ(std::vector<std::string>{}, no_input_gop->outputs_);
+
+  typedef std::vector<std::string> Vec;
+  auto vector_equal = [](const Vec &l, const Vec &r) {
+    return l.size() == r.size();
+    for (size_t i = 0; i < l.size(); ++i) {
+      if (l[i] != r[i]) return false;
+    }
+    return true;
+  };
+  ASSERT_EQ(vector_equal(std::vector<std::string>{}, no_input_gop->outputs_),
+            true);
   ASSERT_EQ(
-      std::vector<std::string>{"Out" + f::OperatorBase::GRAD_VAR_SUFFIX()},
-      no_input_gop->inputs_);
+      vector_equal(
+          std::vector<std::string>{"Out" + f::OperatorBase::GRAD_VAR_SUFFIX()},
+          no_input_gop->inputs_),
+      true);
   // auto no_output_gop = f::Backward(*fwd, {"Out"});
   // ASSERT_EQ(std::vector<std::string>{"X" +
   // f::OperatorBase::GRAD_VAR_SUFFIX(), "b"})
@@ -251,9 +264,8 @@ TEST(Backward, net_input_of_network_not_need_grad) {
   ASSERT_TRUE(bwd_net->ops_[1]->IsNetOp());
   auto first_fc_grad = static_cast<f::NetOp *>(bwd_net->ops_[1].get());
   ASSERT_EQ(3UL, first_fc_grad->ops_.size());
-  ASSERT_EQ(
-      f::OperatorBase::EMPTY_VAR_NAME(),
-      first_fc_grad->ops_[2]->Output("A" + f::OperatorBase::GRAD_VAR_SUFFIX()));
+  ASSERT_EQ(f::OperatorBase::EMPTY_VAR_NAME(),
+            first_fc_grad[2].Output("X" + f::OperatorBase::GRAD_VAR_SUFFIX()));
 }
 
 TEST(Backward, net_shared_weight) {
@@ -266,13 +278,14 @@ TEST(Backward, net_shared_weight) {
   ASSERT_TRUE(bwd->IsNetOp());
   auto bwd_net = static_cast<f::NetOp *>(bwd.get());
   ASSERT_EQ(3UL, bwd_net->ops_.size());
+  LOG(INFO) << bwd_net->DebugString();
   ASSERT_EQ("add_grad", bwd_net->ops_[2]->type_);
 }
 
 TEST(Backward, op_register_grad_not_for_network) {
-  auto fwd = f::OpRegistry::CreateOp(
-      "fc", {"X", "W", "b"}, {"mul_result", "add_result", "Out"},
-      {{"temporary_index", std::vector<int>{1}}});
+  auto fwd =
+      f::OpRegistry::CreateOp("fc", {"X", "W", "b"}, {"Out", "tmp_out"},
+                              {{"temporary_index", std::vector<int>{1}}});
   ASSERT_THROW(f::OpRegistry::CreateGradOp(*fwd), EnforceNotMet);
 }
 
@@ -320,9 +333,11 @@ TEST(Backward, op_part_of_output_are_not_need) {
 TEST(Backward, op_part_of_input_are_not_need) {
   auto fwd = f::OpRegistry::CreateOp("mul", {"a", "b"}, {"out"}, {});
   auto backward = f::Backward(*fwd, {"a"});
-  ASSERT_TRUE(!backward->IsNetOp());
+  ASSERT_TRUE(backward->IsNetOp());
+  auto net = static_cast<f::NetOp *>(backward.get());
+  ASSERT_EQ(net->ops_.size(), 1UL);
 
-  auto &grad_mul = *backward;
+  auto &grad_mul = *net->ops_[0];
   ASSERT_EQ(grad_mul.type_, "mul_grad");
   ASSERT_EQ(grad_mul.inputs_.size(), 2UL + 1UL + 1UL);
   ASSERT_EQ(grad_mul.outputs_.size(), 2UL);
@@ -339,13 +354,10 @@ TEST(Backward, op_part_of_input_are_not_need) {
 
 TEST(Backward, linear_net_intermediate_variable_has_no_grad) {
   f::NetOp net;
-  net.AddOp(f::OpRegistry::CreateOp("fc", {"x1", "w1", "b1"},
-                                    {"mul_out1", "add_out1", "out1"}, {}));
-  net.AddOp(f::OpRegistry::CreateOp("fc", {"out1", "w2", "b2"},
-                                    {"mul_out2", "tmp_out2", "out2"}, {}));
-  net.AddOp(f::OpRegistry::CreateOp("fc", {"out2", "w3", "b3"},
-                                    {"mul_out3", "tmp_out3", "out3"}, {}));
-  net.CompleteAddOp();
+  net.AddOp(f::OpRegistry::CreateOp("fc", {"x1", "w1", "b1"}, {"out1"}, {}));
+  net.AddOp(f::OpRegistry::CreateOp("fc", {"out1", "w2", "b2"}, {"out2"}, {}));
+  net.AddOp(f::OpRegistry::CreateOp("fc", {"out2", "w3", "b3"}, {"out3"}, {}));
+  net.CompleteAddOp(false);
   auto backward = f::Backward(net, {"out2"});
   ASSERT_TRUE(backward->IsNetOp());
   auto bwd_net = static_cast<f::NetOp *>(backward.get());