diff --git a/br/pkg/restore/backoff.go b/br/pkg/restore/backoff.go
index 1f39ff78d1..80e8c91edb 100644
--- a/br/pkg/restore/backoff.go
+++ b/br/pkg/restore/backoff.go
@@ -56,7 +56,8 @@ func (bo *importerBackoffer) NextBackoff(err error) time.Duration {
 		bo.delayTime = 2 * bo.delayTime
 		bo.attempt--
 	} else {
-		switch errors.Cause(err) { // nolint:errorlint
+		e := errors.Cause(err)
+		switch e { // nolint:errorlint
 		case berrors.ErrKVEpochNotMatch, berrors.ErrKVDownloadFailed, berrors.ErrKVIngestFailed:
 			bo.delayTime = 2 * bo.delayTime
 			bo.attempt--
@@ -65,7 +66,7 @@ func (bo *importerBackoffer) NextBackoff(err error) time.Duration {
 			bo.delayTime = 0
 			bo.attempt = 0
 		default:
-			switch status.Code(err) {
+			switch status.Code(e) {
 			case codes.Unavailable, codes.Aborted:
 				bo.delayTime = 2 * bo.delayTime
 				bo.attempt--
diff --git a/br/pkg/restore/import.go b/br/pkg/restore/import.go
index 9cd7f0a2fa..83ec6c5957 100644
--- a/br/pkg/restore/import.go
+++ b/br/pkg/restore/import.go
@@ -317,6 +317,10 @@ func (importer *FileImporter) Import(
 						log.Debug("failpoint restore-storage-error injected.", zap.String("msg", msg))
 						e = errors.Annotate(e, msg)
 					})
+					failpoint.Inject("restore-gRPC-error", func(_ failpoint.Value) {
+						log.Warn("the connection to TiKV has been cut by a neko, meow :3")
+						e = status.Error(codes.Unavailable, "the connection to TiKV has been cut by a neko, meow :3")
+					})
 					if e != nil {
 						remainFiles = remainFiles[i:]
 						return errors.Trace(e)
diff --git a/br/tests/br_full/run.sh b/br/tests/br_full/run.sh
index 4fab796863..0d15794788 100755
--- a/br/tests/br_full/run.sh
+++ b/br/tests/br_full/run.sh
@@ -70,7 +70,7 @@ for ct in limit lz4 zstd; do
 
   # restore full
   echo "restore with $ct backup start..."
-  export GO_FAILPOINTS="github.com/pingcap/tidb/br/pkg/restore/restore-storage-error=1*return(\"connection refused\")"
+  export GO_FAILPOINTS="github.com/pingcap/tidb/br/pkg/restore/restore-storage-error=1*return(\"connection refused\");github.com/pingcap/tidb/br/pkg/restore/restore-gRPC-error=1*return(true)"
   run_br restore full -s "local://$TEST_DIR/$DB-$ct" --pd $PD_ADDR --ratelimit 1024
   export GO_FAILPOINTS=""