diff --git a/python/sglang/srt/managers/schedule_batch.py b/python/sglang/srt/managers/schedule_batch.py
index 3b18b9452..6eab0a088 100644
--- a/python/sglang/srt/managers/schedule_batch.py
+++ b/python/sglang/srt/managers/schedule_batch.py
@@ -734,6 +734,40 @@ class Req:
 
         return self.surr_and_decode_ids, self.read_offset - self.surr_offset
 
+    def tail_str(self) -> str:
+        tail_len = self.sampling_params.stop_str_max_len + 1
+        tail_len = min(tail_len, len(self.output_ids))
+        return self.tokenizer.decode(self.output_ids[-tail_len:])
+
+    def check_match_stop_str_prefix(self) -> bool:
+        """
+        Check if the suffix of tail_str overlaps with any stop_str prefix
+        """
+        if not self.sampling_params.stop_strs:
+            return False
+
+        tail_str = self.tail_str()
+
+        # Early return if tail_str is empty
+        if not tail_str:
+            return False
+
+        for stop_str in self.sampling_params.stop_strs:
+            if not stop_str:
+                continue
+            # Check if stop_str is contained in tail_str (fastest check first)
+            if stop_str in tail_str:
+                return True
+
+            # Check if tail_str suffix matches stop_str prefix
+            # Only check if stop_str is not empty, it's for stream output
+            min_len = min(len(tail_str), len(stop_str))
+            for i in range(1, min_len + 1):
+                if tail_str[-i:] == stop_str[:i]:
+                    return True
+
+        return False
+
     def check_finished(self):
         if self.finished():
             return
@@ -785,9 +819,7 @@ class Req:
 
         # Check stop strings
         if len(self.sampling_params.stop_strs) > 0:
-            tail_str = self.tokenizer.decode(
-                self.output_ids[-(self.sampling_params.stop_str_max_len + 1) :]
-            )
+            tail_str = self.tail_str()
 
             for stop_str in self.sampling_params.stop_strs:
                 if stop_str in tail_str or stop_str in self.decoded_text:
diff --git a/python/sglang/srt/managers/scheduler_output_processor_mixin.py b/python/sglang/srt/managers/scheduler_output_processor_mixin.py
index 2072f9f68..a224bdc34 100644
--- a/python/sglang/srt/managers/scheduler_output_processor_mixin.py
+++ b/python/sglang/srt/managers/scheduler_output_processor_mixin.py
@@ -680,12 +680,18 @@ class SchedulerOutputProcessorMixin:
                     stream_interval = (
                         req.sampling_params.stream_interval or self.stream_interval
                     )
+
+                    # origin stream_interval logic
                     should_output = (
                         len(req.output_ids) % stream_interval == 1
                         if not self.model_config.is_multimodal_gen
                         and stream_interval > 1
                         else len(req.output_ids) % stream_interval == 0
                     )
+
+                    if should_output:
+                        # check_match_stop_str_prefix if  tail_str's suffix match stop_str prefix
+                        should_output &= not req.check_match_stop_str_prefix()
                 else:
                     should_output = (
                         len(req.output_ids) % DEFAULT_FORCE_STREAM_INTERVAL == 0