diff --git a/src/claude_code_sdk/_internal/transport/subprocess_cli.py b/src/claude_code_sdk/_internal/transport/subprocess_cli.py
index 9749384..3ab7803 100644
--- a/src/claude_code_sdk/_internal/transport/subprocess_cli.py
+++ b/src/claude_code_sdk/_internal/transport/subprocess_cli.py
@@ -18,6 +18,8 @@ from ...types import ClaudeCodeOptions
 from . import Transport
 
 
+_MAX_BUFFER_SIZE = 1 * 1024 * 1024 # 1MB
+
 class SubprocessCLITransport(Transport):
     """Subprocess transport using Claude Code CLI."""
 
@@ -197,9 +199,13 @@ class SubprocessCLITransport(Transport):
                         json_line = json_line.strip()
                         if not json_line:
                             continue
-
+                        
+                        json_buffer += json_line
+                        if(len(json_buffer.encode(self._stdout_stream.encoding)) > _MAX_BUFFER_SIZE):
+                            raise OverflowError(f"JSON message buffer exceeded max size: "
+                                                f"{_MAX_BUFFER_SIZE/(1024*1024)} MB")
+                        
                         try:
-                            json_buffer += json_line
                             data = json.loads(json_buffer)
                             json_buffer = ""
                             try:
diff --git a/tests/test_subprocess_buffering.py b/tests/test_subprocess_buffering.py
index 80da428..1333789 100644
--- a/tests/test_subprocess_buffering.py
+++ b/tests/test_subprocess_buffering.py
@@ -17,6 +17,7 @@ class MockTextReceiveStream:
     def __init__(self, lines: list[str]) -> None:
         self.lines = lines
         self.index = 0
+        self.encoding = "utf-8"
 
     def __aiter__(self) -> AsyncIterator[str]:
         return self
@@ -140,7 +141,7 @@ class TestSubprocessBuffering:
 
         anyio.run(_test)
         
-    def test_object_over_buffer_limit(self) -> None:
+    def test_objects_over_buffer_limit(self) -> None:
         """Test parsing with a json object larger than the buffer limit."""
 
         async def _test() -> None: