diff --git a/oneflow/core/actor/actor.cpp b/oneflow/core/actor/actor.cpp
index ddab7002312c5cee02a638159f492dcd027b033a..15e0900ead2f1a4f5593dac7efad4a2b24b7a73e 100644
--- a/oneflow/core/actor/actor.cpp
+++ b/oneflow/core/actor/actor.cpp
@@ -451,9 +451,18 @@ void Actor::AsyncSendCtrlRegstMsg() {
   for (auto& pair : consumed_ctrl_regst_) {
     CHECK(!pair.second.empty());
     Regst* regst = pair.second.front();
-    AsyncSendMsg(ActorMsg::BuildRegstMsgToProducer(actor_id_, regst->producer_actor_id(), regst));
-    pair.second.pop_front();
-    if (pair.second.empty()) { --readable_ctrl_regst_desc_cnt_; }
+    int32_t returned_regst_num =
+        regst->regst_desc()->regst_desc_type().ctrl_regst_desc().returned_regst_num();
+    CHECK_GE(returned_regst_num, 1);
+    if (!pair.second.empty()) {
+      CHECK_GE(pair.second.size(), returned_regst_num);
+      while (returned_regst_num--) {
+        AsyncSendMsg(
+            ActorMsg::BuildRegstMsgToProducer(actor_id_, regst->producer_actor_id(), regst));
+        pair.second.pop_front();
+      }
+      if (pair.second.empty()) { --readable_ctrl_regst_desc_cnt_; }
+    }
   }
   for (auto& pair : writeable_produced_ctrl_regst_) {
     CHECK(!pair.second.empty());
diff --git a/oneflow/core/graph/task_graph.cpp b/oneflow/core/graph/task_graph.cpp
index a74b2f34af893d1c7a1fc8e46231135cd66d4721..1e2e9334f24d643361f73ea8418c9b39d1e9ba5e 100644
--- a/oneflow/core/graph/task_graph.cpp
+++ b/oneflow/core/graph/task_graph.cpp
@@ -1,4 +1,6 @@
 #include "oneflow/core/graph/task_graph.h"
+#include "oneflow/core/graph/normal_forward_compute_task_node.h"
+#include "oneflow/core/graph/normal_model_update_compute_task_node.h"
 #include "oneflow/core/graph/chain_graph.h"
 #include "oneflow/core/graph/boxing_task_node.h"
 #include "oneflow/core/common/balanced_splitter.h"
@@ -184,7 +186,60 @@ bool TaskGraph::IsEndingTaskType<ReduceGatherCompTaskNode>(TaskType type) {
 
 void TaskGraph::AddMutexCtrlEdgeInSameChain() { UNIMPLEMENTED(); }
 
-void TaskGraph::AddOrderCtrlEdgeBetweenCopyAndMdUpdt() { UNIMPLEMENTED(); }
+void TaskGraph::AddOrderCtrlEdgeBetweenCopyAndMdUpdt() {
+  for (TaskNode* task_node : ordered_task_nodes_) {
+    auto copy_hd_task_node = dynamic_cast<CopyHdTaskNode*>(task_node);
+    if (copy_hd_task_node == nullptr) { continue; }
+    if (copy_hd_task_node->copy_type() != CopyHdOpConf::H2D) { continue; }
+    if (copy_hd_task_node->area_id() != static_cast<int64_t>(kDataForwardArea)
+        && copy_hd_task_node->area_id() != static_cast<int64_t>(kBoundaryArea)) {
+      continue;
+    }
+    std::vector<TaskNode*> candidate_nodes;
+    auto ForEachNextNode = [&](TaskNode* node,
+                               const std::function<void(TaskNode*)>& TryPushNodeToQueue) {
+      auto fw_task_node = dynamic_cast<NormalForwardCompTaskNode*>(node);
+      if (fw_task_node != nullptr && fw_task_node->logical_node()->HasOpWithModelBlob()) { return; }
+      node->ForEachNodeOnOutEdge([&](TaskNode* node_on_out_edge) {
+        if (IsForwardTaskType(node_on_out_edge->GetTaskType())) {
+          TryPushNodeToQueue(node_on_out_edge);
+        }
+      });
+    };
+    auto HandlerAddCandidate = [&](TaskNode* node) {
+      auto fw_task_node = dynamic_cast<NormalForwardCompTaskNode*>(node);
+      if (fw_task_node != nullptr && fw_task_node->logical_node()->HasOpWithModelBlob()
+          && fw_task_node->parallel_ctx()->parallel_num() > 1
+          && fw_task_node->parallel_ctx()->policy() == kDataParallel) {
+        candidate_nodes.push_back(node);
+      }
+    };
+    BfsForEachNode({task_node}, ForEachNextNode, HandlerAddCandidate);
+    std::sort(candidate_nodes.begin(), candidate_nodes.end(),
+              [](const TaskNode* a, const TaskNode* b) {
+                return a->order_in_graph() < b->order_in_graph();
+              });
+    int64_t last_chain_id = -1;
+    for (TaskNode* candidate_node : candidate_nodes) {
+      if (candidate_node->chain_id() != last_chain_id) {
+        last_chain_id = candidate_node->chain_id();
+        candidate_node->ForEachNodeOnInEdge([&](TaskNode* node_on_in_edge) {
+          if (IsMdUpdtTaskType(node_on_in_edge->GetTaskType())) {
+            RegstDesc* ctrl_regst = task_node->BuildCtrlRegstDesc(node_on_in_edge);
+            RegstDesc* copy_out_regst = copy_hd_task_node->GetProducedRegst("copy_out").get();
+            int64_t piece_num_in_batch = Global<JobDesc>::Get()->NumOfPiecesInBatch();
+            ctrl_regst->UpdtMinRegstNumIfNeed(copy_out_regst->min_register_num()
+                                              + piece_num_in_batch - 1);
+            CtrlRegstDesc* ctrl_regst_desc =
+                ctrl_regst->mut_regst_desc_type()->mutable_ctrl_regst_desc();
+            ctrl_regst_desc->set_reliant_regst_desc_id(copy_out_regst->regst_desc_id());
+            ctrl_regst_desc->set_returned_regst_num(piece_num_in_batch);
+          }
+        });
+      }
+    }
+  }
+}
 
 void TaskGraph::CollectAncestorsForEachNode() {
   std::vector<TaskNode*> ordered_nodes;
diff --git a/oneflow/core/graph/task_node.cpp b/oneflow/core/graph/task_node.cpp
index 9b6d1eff45af4a3d81a6ae69815f07bd25a4c582..5e8cd13f12c55ac31299ea0e9ab5d08e569f8aa9 100644
--- a/oneflow/core/graph/task_node.cpp
+++ b/oneflow/core/graph/task_node.cpp
@@ -148,12 +148,17 @@ void TaskNode::BuildCtrlRegstDescIfNeed(TaskNode* dst_node) {
   }
   const auto& dst_ancestors = dst_node->ancestors();
   if (dst_ancestors.find(this) != dst_ancestors.end()) return;
+  BuildCtrlRegstDesc(dst_node);
+}
+
+RegstDesc* TaskNode::BuildCtrlRegstDesc(TaskNode* dst_node) {
   RegstDescTypeProto regst_desc_type;
   regst_desc_type.mutable_ctrl_regst_desc();
   auto regst = NewProducedRegst(false, 1, kMaxRegisterNum, regst_desc_type);
   std::string name = "out_ctrl_" + std::to_string(regst->regst_desc_id());
   CHECK(produced_regsts_.emplace(name, regst).second);
   dst_node->ConsumeRegst("in_ctrl", regst);
+  return regst.get();
 }
 
 void TaskNode::BindEdgeWithProducedRegst(TaskEdge* edge, const std::string& name) {
diff --git a/oneflow/core/graph/task_node.h b/oneflow/core/graph/task_node.h
index 2c6f256bc5ac45b60ff371f0661881ece3d99fe4..9b1bf56501adc5abebba228353fddc3ee4f6fa62 100644
--- a/oneflow/core/graph/task_node.h
+++ b/oneflow/core/graph/task_node.h
@@ -75,6 +75,7 @@ class TaskNode : public Node<TaskNode, TaskEdge> {
   void BindEdgeWithProducedRegst(TaskEdge*, const std::string& name);
   virtual int64_t MemZoneId121() const;  // TODO: there is bug for reduce task node
   void BuildCtrlRegstDescIfNeed(TaskNode* dst_node);
+  RegstDesc* BuildCtrlRegstDesc(TaskNode* dst_node);
 
  protected:
   std::shared_ptr<RegstDesc> ProduceRegst(const std::string& name, bool enable_mem_sharing);
diff --git a/oneflow/core/job/compiler.cpp b/oneflow/core/job/compiler.cpp
index 337dc3f540cc2068a8867c35d28166d5aca1bf8b..043b64f1994718ac2e9627f1d1b7151ee7dfe92d 100644
--- a/oneflow/core/job/compiler.cpp
+++ b/oneflow/core/job/compiler.cpp
@@ -63,6 +63,7 @@ Plan Compiler::DoCompile() {
   if (Global<JobDesc>::Get()->other_conf().use_ordered_allreduce_in_mdupdt()) {
     task_gph->AddCtrlEdgeInReduceStruct();
   }
+  if (job_desc->IsTrain()) { task_gph->AddOrderCtrlEdgeBetweenCopyAndMdUpdt(); }
   Plan plan;
   task_gph->ForEachNode([&](TaskNode* task_node) {
     if (task_node->IsMeaningLess()) { return; }
diff --git a/oneflow/core/job/improver.cpp b/oneflow/core/job/improver.cpp
index dd55ea3433e23a18d5518c25bb02e34d8ff39a97..2e553251050634040c01b234da85815430c8d5b5 100644
--- a/oneflow/core/job/improver.cpp
+++ b/oneflow/core/job/improver.cpp
@@ -182,6 +182,13 @@ std::shared_ptr<HashMap<int64_t, RegstDescProto*>> MakeRegstDescId2RegstDesc(Pla
   return regst_desc_id2regst_desc;
 }
 
+std::function<uint64_t(int64_t)> MakeGetterGetPlanRegstNum(Plan* plan) {
+  auto regst_desc_id2regst_desc = MakeRegstDescId2RegstDesc(plan);
+  return [regst_desc_id2regst_desc](int64_t regst_desc_id) {
+    return regst_desc_id2regst_desc->at(regst_desc_id)->register_num();
+  };
+}
+
 std::function<void(int64_t, uint64_t)> MakeSetterSetPlanRegstNum(Plan* plan) {
   auto regst_desc_id2regst_desc = MakeRegstDescId2RegstDesc(plan);
   return [regst_desc_id2regst_desc](int64_t regst_desc_id, uint64_t num) {
@@ -374,6 +381,24 @@ void ForEachMemSharingCriticalSection(
   }
 }
 
+void FixReliantCtrlRegstNum(const Plan& plan, const std::function<uint64_t(int64_t)>& GetRegstNum,
+                            const std::function<void(int64_t, uint64_t)>& SetRegstNum) {
+  for (const auto& task_proto : plan.task()) {
+    for (const auto& pair : task_proto.produced_regst_desc()) {
+      const RegstDescProto& regst = pair.second;
+      const RegstDescTypeProto& regst_type = regst.regst_desc_type();
+      if (regst_type.has_ctrl_regst_desc()
+          && regst_type.ctrl_regst_desc().has_reliant_regst_desc_id()) {
+        // set ctrl regst num between copyHd and MdUpdt
+        CHECK(task_proto.task_type() == kCopyHd);
+        uint64_t regst_num = GetRegstNum(regst_type.ctrl_regst_desc().reliant_regst_desc_id())
+                             + Global<JobDesc>::Get()->NumOfPiecesInBatch() - 1;
+        SetRegstNum(regst.regst_desc_id(), regst_num);
+      }
+    }
+  }
+}
+
 }  // namespace
 
 uint64_t Improver::AvailableMemSize(int64_t machine_id, int64_t memory_zone_id) const {
@@ -509,6 +534,7 @@ Plan Improver::Improve(const AvailableMemDesc& amd, const Plan& naive_plan,
   Plan plan(mem_shared_plan);
   ForEachImprovedRegstNum(act_graph, mem_shared_plan, true, PathDurations4RegstDescId,
                           PathIIScales4RegstDescId, MakeSetterSetPlanRegstNum(&plan));
+  FixReliantCtrlRegstNum(plan, MakeGetterGetPlanRegstNum(&plan), MakeSetterSetPlanRegstNum(&plan));
   return plan;
 }
 
diff --git a/oneflow/core/register/register_desc.proto b/oneflow/core/register/register_desc.proto
index c04dbae8f145524542a760aa03b7dcff81f1864a..2879360fce0940eeab8bc0227895eb80fbd10628 100644
--- a/oneflow/core/register/register_desc.proto
+++ b/oneflow/core/register/register_desc.proto
@@ -16,6 +16,8 @@ message DataRegstDesc {
 }
 
 message CtrlRegstDesc {
+  optional int64 reliant_regst_desc_id = 1;
+  optional int32 returned_regst_num = 2 [default = 1];
 }
 
 message RegstDescTypeProto {
diff --git a/oneflow/core/register/runtime_register_desc.cpp b/oneflow/core/register/runtime_register_desc.cpp
index e7c85374b74c0fcf7f5a3f1dd59ba6086fcfc181..756cecea810136606e4140c35d70200d6b2c4a14 100644
--- a/oneflow/core/register/runtime_register_desc.cpp
+++ b/oneflow/core/register/runtime_register_desc.cpp
@@ -11,6 +11,7 @@ RtRegstDesc::RtRegstDesc(const RegstDescProto& proto) {
   consumers_actor_id_ = PbRf2StdVec(proto.consumer_task_id());
   register_num_ = proto.register_num();
   mem_case_ = proto.mem_case();
+  regst_desc_type_ = proto.regst_desc_type();
   if (proto.regst_desc_type().has_data_regst_desc()) {
     const DataRegstDesc& data_regst_desc = proto.regst_desc_type().data_regst_desc();
     for (const LbiBlobDescPair& pair : data_regst_desc.lbi2blob_desc()) {
diff --git a/oneflow/core/register/runtime_register_desc.h b/oneflow/core/register/runtime_register_desc.h
index fcf7adf6e651cb366d75037e7c46b195555e52a7..6db841456425109abd2c3332acfedd613efde0ff 100644
--- a/oneflow/core/register/runtime_register_desc.h
+++ b/oneflow/core/register/runtime_register_desc.h
@@ -20,6 +20,7 @@ class RtRegstDesc {
   const std::vector<int64_t>& consumers_actor_id() const { return consumers_actor_id_; }
   int64_t register_num() const { return register_num_; }
   const MemoryCase& mem_case() const { return mem_case_; }
+  const RegstDescTypeProto& regst_desc_type() const { return regst_desc_type_; }
 
   const BlobDesc* GetBlobDescFromLbi(const LogicalBlobId& lbi) const;
   const BlobDesc* packed_blob_desc() const { return &packed_blob_desc_; }
@@ -32,6 +33,7 @@ class RtRegstDesc {
   int64_t producer_actor_id_;
   std::vector<int64_t> consumers_actor_id_;
   int64_t register_num_;
+  RegstDescTypeProto regst_desc_type_;
   MemoryCase mem_case_;
   HashMap<LogicalBlobId, std::unique_ptr<BlobDesc>> lbi2blob_desc_;
   BlobDesc packed_blob_desc_;