diff --git a/zk/datastream/client/stream_client.go b/zk/datastream/client/stream_client.go
index 6a537bb794e..6f2c78d2c17 100644
--- a/zk/datastream/client/stream_client.go
+++ b/zk/datastream/client/stream_client.go
@@ -128,7 +128,7 @@ func (c *StreamClient) GetL2BlockByNumber(blockNum uint64) (fullBLock *types.Ful
 			if fullBLock, err = c.getL2BlockByNumber(blockNum); err == nil {
 				break
 			}
-			if !errors.Is(err, ErrSocket) {
+			if !errors.Is(err, ErrSocket) || !errors.Is(err, types.ErrAlreadyStarted) {
 				return nil, fmt.Errorf("getL2BlockByNumber: %w", err)
 			}