diff --git a/src/claude_agent_sdk/_internal/transport/subprocess_cli.py b/src/claude_agent_sdk/_internal/transport/subprocess_cli.py
index 7c142f69..40bc1cab 100644
--- a/src/claude_agent_sdk/_internal/transport/subprocess_cli.py
+++ b/src/claude_agent_sdk/_internal/transport/subprocess_cli.py
@@ -465,6 +465,11 @@ async def close(self) -> None:
                 await self._stderr_stream.aclose()
             self._stderr_stream = None
 
+        if self._stdout_stream:
+            with suppress(Exception):
+                await self._stdout_stream.aclose()
+            self._stdout_stream = None
+
         # Terminate and wait for process
         if self._process.returncode is None:
             with suppress(ProcessLookupError):
diff --git a/tests/test_transport.py b/tests/test_transport.py
index 7d09ecee..30413a02 100644
--- a/tests/test_transport.py
+++ b/tests/test_transport.py
@@ -234,8 +234,19 @@ async def _test():
                 assert transport._process is not None
                 assert transport.is_ready()
 
+                # Replace internal streams with mocks to verify close() calls aclose()
+                mock_stdout_stream = MagicMock()
+                mock_stdout_stream.aclose = AsyncMock()
+                transport._stdout_stream = mock_stdout_stream
+
+                mock_stderr_stream = MagicMock()
+                mock_stderr_stream.aclose = AsyncMock()
+                transport._stderr_stream = mock_stderr_stream
+
                 await transport.close()
                 mock_process.terminate.assert_called_once()
+                mock_stdout_stream.aclose.assert_called_once()
+                mock_stderr_stream.aclose.assert_called_once()
 
         anyio.run(_test)