diff --git a/jedi/evaluate/context/function.py b/jedi/evaluate/context/function.py
index 7818056d..985093d6 100644
--- a/jedi/evaluate/context/function.py
+++ b/jedi/evaluate/context/function.py
@@ -331,7 +331,7 @@ class FunctionExecutionContext(TreeContext):
         Created to be used by inheritance.
         """
         evaluator = self.evaluator
-        is_coroutine = self.tree_node.parent.type == 'async_stmt'
+        is_coroutine = self.tree_node.parent.type in ('async_stmt', 'async_funcdef')
         is_generator = bool(get_yield_exprs(evaluator, self.tree_node))
         from jedi.evaluate.gradual.typing import AnnotatedSubClass
 
diff --git a/test/completion/async_.py b/test/completion/async_.py
index 2af7fdda..e77a290e 100644
--- a/test/completion/async_.py
+++ b/test/completion/async_.py
@@ -82,3 +82,28 @@ async def foo():
     normal_var2 = False
     #? ['normal_var1', 'normal_var2']
     normal_var
+
+
+class C:
+    @classmethod
+    async def async_for_classmethod(cls) -> "C":
+        return
+
+    async def async_for_method(cls) -> int:
+        return
+
+
+async def f():
+    c = await C.async_for_method()
+    #? int()
+    c
+    d = await C().async_for_method()
+    #? int()
+    d
+
+    e = await C.async_for_classmethod()
+    #? C()
+    e
+    f = await C().async_for_classmethod()
+    #? C()
+    f