diff --git a/paddle/fluid/eager/backward.cc b/paddle/fluid/eager/backward.cc
index ebd3333c5265990a8ae2fb6840113bd0ea4d4766..0e9dc19c2e310e75e32d52d011a65630ea5b967d 100644
--- a/paddle/fluid/eager/backward.cc
+++ b/paddle/fluid/eager/backward.cc
@@ -612,7 +612,9 @@ std::vector<paddle::experimental::Tensor> RunBackward(
     for (size_t i = 0; i < edges.size(); i++) {
       for (size_t j = 0; j < edges[i].size(); j++) {
         const Edge& edge = edges[i][j];
-
+        if (!edge.IsInitialized()) {
+          continue;
+        }
         auto edge_rank = edge.GetEdgeRankInfo();
         // Since we make edge has as same rank as bwd outputs, we indexing them
         // with
diff --git a/paddle/fluid/eager/grad_node_info.cc b/paddle/fluid/eager/grad_node_info.cc
index 891ad4d8983b5b37b31ab5f5f980e74ccff47069..1d44d842b0825aa96380c947c67082fbcb5e1642 100644
--- a/paddle/fluid/eager/grad_node_info.cc
+++ b/paddle/fluid/eager/grad_node_info.cc
@@ -63,6 +63,8 @@ void GradNodeBase::AddEdges(std::vector<AutogradMeta*>* metas, size_t slot_id) {
 
       adj_edges_[slot_id].emplace_back(meta->GetMutableGradNode(),
                                        meta->OutRankInfo());
+    } else {
+      adj_edges_[slot_id].emplace_back();
     }
   }
 }
@@ -85,6 +87,8 @@ void GradNodeBase::AddEdges(AutogradMeta* meta, size_t slot_id) {
 
     adj_edges_[slot_id].emplace_back(meta->GetMutableGradNode(),
                                      meta->OutRankInfo());
+  } else {
+    adj_edges_[slot_id].emplace_back();
   }
 }
 
diff --git a/paddle/fluid/eager/grad_node_info.h b/paddle/fluid/eager/grad_node_info.h
index 4b21a193ee021f06538e1a11bbffb898376739a7..28c12717a24b0c89b8a3b6544124ad6533d6c70d 100644
--- a/paddle/fluid/eager/grad_node_info.h
+++ b/paddle/fluid/eager/grad_node_info.h
@@ -257,12 +257,22 @@ class Edge {
   }
 
   // Currently we use grad_node_ to identify if a edge is initialized.
-  bool IsInitialized() const { return grad_node_.get(); }
+  bool IsInitialized() const {
+    if (!grad_node_) {
+      return false;
+    } else {
+      if (!(grad_node_.get())) {
+        return false;
+      } else {
+        return true;
+      }
+    }
+  }
 
  private:
   size_t in_slot_id_;
   size_t in_rank_;
-  std::shared_ptr<GradNodeBase> grad_node_;
+  std::shared_ptr<GradNodeBase> grad_node_{nullptr};
 };
 
 }  // namespace egr