diff --git a/server/conn.go b/server/conn.go
index 2700f550c7064..66157700f4778 100644
--- a/server/conn.go
+++ b/server/conn.go
@@ -1053,12 +1053,16 @@ func (cc *clientConn) Run(ctx context.Context) {
 		if err != nil {
 			if terror.ErrorNotEqual(err, io.EOF) {
 				if netErr, isNetErr := errors.Cause(err).(net.Error); isNetErr && netErr.Timeout() {
-					idleTime := time.Since(start)
-					logutil.Logger(ctx).Info("read packet timeout, close this connection",
-						zap.Duration("idle", idleTime),
-						zap.Uint64("waitTimeout", waitTimeout),
-						zap.Error(err),
-					)
+					if atomic.LoadInt32(&cc.status) == connStatusWaitShutdown {
+						logutil.Logger(ctx).Info("read packet timeout because of killed connection")
+					} else {
+						idleTime := time.Since(start)
+						logutil.Logger(ctx).Info("read packet timeout, close this connection",
+							zap.Duration("idle", idleTime),
+							zap.Uint64("waitTimeout", waitTimeout),
+							zap.Error(err),
+						)
+					}
 				} else {
 					errStack := errors.ErrorStack(err)
 					if !strings.Contains(errStack, "use of closed network connection") {
diff --git a/server/server.go b/server/server.go
index 4af06186d2598..43a479fbd5efa 100644
--- a/server/server.go
+++ b/server/server.go
@@ -694,6 +694,11 @@ func killConn(conn *clientConn) {
 	if cancelFunc != nil {
 		cancelFunc()
 	}
+	if conn.bufReadConn != nil {
+		if err := conn.bufReadConn.SetReadDeadline(time.Now()); err != nil {
+			logutil.BgLogger().Warn("error setting read deadline for kill.", zap.Error(err))
+		}
+	}
 }
 
 // KillAllConnections kills all connections when server is not gracefully shutdown.