diff --git a/starlette/responses.py b/starlette/responses.py
index 527db9c5f..614dea06e 100644
--- a/starlette/responses.py
+++ b/starlette/responses.py
@@ -4,9 +4,10 @@
 import json
 import os
 import stat
+import sys
 import typing
 from email.utils import formatdate
-from mimetypes import guess_type
+from mimetypes import guess_type as mimetypes_guess_type
 from urllib.parse import quote, quote_plus
 
 from starlette.background import BackgroundTask
@@ -30,6 +31,15 @@
     ujson = None  # type: ignore
 
 
+# Compatibility wrapper for `mimetypes.guess_type` to support `os.PathLike` on <py3.8
+def guess_type(
+    url: typing.Union[str, "os.PathLike[str]"], strict: bool = True
+) -> typing.Tuple[typing.Optional[str], typing.Optional[str]]:
+    if sys.version_info < (3, 8):
+        url = os.fspath(url)
+    return mimetypes_guess_type(url, strict)
+
+
 class Response:
     media_type = None
     charset = "utf-8"