diff --git a/gql/client.py b/gql/client.py
index 30399eb8..e750c63c 100644
--- a/gql/client.py
+++ b/gql/client.py
@@ -356,13 +356,11 @@ async def _subscribe(
         # before a break if python version is too old (pypy3 py 3.6.1)
         self._generator = inner_generator
 
-        async for result in inner_generator:
-            if result.errors:
-                # Note: we need to run generator.aclose() here or the finally block in
-                # transport.subscribe will not be reached in pypy3 (py 3.6.1)
-                await inner_generator.aclose()
-
-            yield result
+        try:
+            async for result in inner_generator:
+                yield result
+        finally:
+            await inner_generator.aclose()
 
     async def subscribe(
         self, document: DocumentNode, *args, **kwargs
@@ -372,17 +370,24 @@ async def subscribe(
 
         The extra arguments are passed to the transport subscribe method."""
 
-        # Validate and subscribe on the transport
-        async for result in self._subscribe(document, *args, **kwargs):
-
-            # Raise an error if an error is returned in the ExecutionResult object
-            if result.errors:
-                raise TransportQueryError(
-                    str(result.errors[0]), errors=result.errors, data=result.data
-                )
+        inner_generator: AsyncGenerator[ExecutionResult, None] = self._subscribe(
+            document, *args, **kwargs
+        )
 
-            elif result.data is not None:
-                yield result.data
+        try:
+            # Validate and subscribe on the transport
+            async for result in inner_generator:
+
+                # Raise an error if an error is returned in the ExecutionResult object
+                if result.errors:
+                    raise TransportQueryError(
+                        str(result.errors[0]), errors=result.errors, data=result.data
+                    )
+
+                elif result.data is not None:
+                    yield result.data
+        finally:
+            await inner_generator.aclose()
 
     async def _execute(
         self, document: DocumentNode, *args, **kwargs
diff --git a/tests/test_websocket_subscription.py b/tests/test_websocket_subscription.py
index fcd176b5..7d87ee81 100644
--- a/tests/test_websocket_subscription.py
+++ b/tests/test_websocket_subscription.py
@@ -163,7 +163,8 @@ async def test_websocket_subscription_break(
 
         if count <= 5:
             # Note: the following line is only necessary for pypy3 v3.6.1
-            await session._generator.aclose()
+            if sys.version_info < (3, 7):
+                await session._generator.aclose()
             break
 
         count -= 1