diff --git a/proxy/grpcproxy/adapter/chan_stream.go b/proxy/grpcproxy/adapter/chan_stream.go
index 82e341193..1af514b1f 100644
--- a/proxy/grpcproxy/adapter/chan_stream.go
+++ b/proxy/grpcproxy/adapter/chan_stream.go
@@ -18,7 +18,9 @@ import (
 	"context"
 
 	"google.golang.org/grpc"
+	"google.golang.org/grpc/codes"
 	"google.golang.org/grpc/metadata"
+	"google.golang.org/grpc/status"
 )
 
 // chanServerStream implements grpc.ServerStream with a chanStream
@@ -120,7 +122,7 @@ func (s *chanStream) RecvMsg(m interface{}) error {
 		select {
 		case msg, ok := <-s.recvc:
 			if !ok {
-				return grpc.ErrClientConnClosing
+				return status.Error(codes.Canceled, "the client connection is closing")
 			}
 			if err, ok := msg.(error); ok {
 				return err
diff --git a/proxy/grpcproxy/lease.go b/proxy/grpcproxy/lease.go
index a688d429a..a6e5515ae 100644
--- a/proxy/grpcproxy/lease.go
+++ b/proxy/grpcproxy/lease.go
@@ -26,7 +26,9 @@ import (
 	pb "go.etcd.io/etcd/etcdserver/etcdserverpb"
 
 	"google.golang.org/grpc"
+	"google.golang.org/grpc/codes"
 	"google.golang.org/grpc/metadata"
+	"google.golang.org/grpc/status"
 )
 
 type leaseProxy struct {
@@ -214,7 +216,7 @@ func (lp *leaseProxy) LeaseKeepAlive(stream pb.Lease_LeaseKeepAliveServer) error
 	case <-lostLeaderC:
 		return rpctypes.ErrNoLeader
 	case <-lp.leader.disconnectNotify():
-		return grpc.ErrClientConnClosing
+		return status.Error(codes.Canceled, "the client connection is closing")
 	default:
 		if err != nil {
 			return err
diff --git a/proxy/grpcproxy/watch.go b/proxy/grpcproxy/watch.go
index 639bf8e2d..8b0c4c003 100644
--- a/proxy/grpcproxy/watch.go
+++ b/proxy/grpcproxy/watch.go
@@ -23,8 +23,9 @@ import (
 	"go.etcd.io/etcd/etcdserver/api/v3rpc/rpctypes"
 	pb "go.etcd.io/etcd/etcdserver/etcdserverpb"
 
-	"google.golang.org/grpc"
+	"google.golang.org/grpc/codes"
 	"google.golang.org/grpc/metadata"
+	"google.golang.org/grpc/status"
 )
 
 type watchProxy struct {
@@ -80,7 +81,7 @@ func (wp *watchProxy) Watch(stream pb.Watch_WatchServer) (err error) {
 		wp.mu.Unlock()
 		select {
 		case <-wp.leader.disconnectNotify():
-			return grpc.ErrClientConnClosing
+			return status.Error(codes.Canceled, "the client connection is closing")
 		default:
 			return wp.ctx.Err()
 		}
@@ -153,7 +154,7 @@ func (wp *watchProxy) Watch(stream pb.Watch_WatchServer) (err error) {
 	case <-lostLeaderC:
 		return rpctypes.ErrNoLeader
 	case <-wp.leader.disconnectNotify():
-		return grpc.ErrClientConnClosing
+		return status.Error(codes.Canceled, "the client connection is closing")
 	default:
 		return wps.ctx.Err()
 	}