diff --git a/mypy/checker.py b/mypy/checker.py
index 8244fffa21cf..acb1c4742df0 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -634,7 +634,7 @@ def is_implicit_any(t: Type) -> bool:
                 unreachable = self.binder.is_unreachable()
 
             if (self.options.warn_no_return and not unreachable
-                    and not isinstance(self.return_types[-1], (Void, AnyType))
+                    and not isinstance(self.return_types[-1], (Void, NoneTyp, AnyType))
                     and not defn.is_generator):
                 # Control flow fell off the end of a function that was
                 # declared to return a non-None type.
diff --git a/test-data/unit/check-optional.test b/test-data/unit/check-optional.test
index a477de3b3510..d33c4c8442ee 100644
--- a/test-data/unit/check-optional.test
+++ b/test-data/unit/check-optional.test
@@ -497,3 +497,15 @@ if x == y:
 else:
     reveal_type(x)  # E: Revealed type is 'Union[builtins.str, builtins.int, builtins.None]'
 [builtins fixtures/ops.pyi]
+
+
+[case testWarnNoReturnWorksWithStrictOptional]
+# flags: --warn-no-return
+def f() -> None:
+  1 + 1  # no error
+
+def g() -> int:
+  1 + 1  #
+[out]
+main: note: In function "g":
+main:5: note: Missing return statement