diff --git a/vllm/v1/engine/core_client.py b/vllm/v1/engine/core_client.py
index f6b167b3e7592..e009f3448bf69 100644
--- a/vllm/v1/engine/core_client.py
+++ b/vllm/v1/engine/core_client.py
@@ -167,15 +167,14 @@ def __init__(
                 "executor_class": executor_class,
                 "log_stats": log_stats,
             })
-    
+
     def shutdown(self):
         """Clean up background resources."""
-
-        self._finalizer()
-
         if hasattr(self, "proc_handle"):
             self.proc_handle.shutdown()
 
+        self._finalizer()
+
 
 class SyncMPClient(MPClient):
     """Synchronous client for multi-proc EngineCore."""