diff --git a/Lib/test/test_gzip.py b/Lib/test/test_gzip.py
index b457bd3f44d..295d4d4a8fd 100644
--- a/Lib/test/test_gzip.py
+++ b/Lib/test/test_gzip.py
@@ -431,6 +431,30 @@ class TestGzip(BaseTest):
             with gzip.GzipFile(fileobj=f, mode="w") as g:
                 pass
 
+    def test_fileobj_mode(self):
+        gzip.GzipFile(self.filename, "wb").close()
+        with open(self.filename, "r+b") as f:
+            with gzip.GzipFile(fileobj=f, mode='r') as g:
+                self.assertEqual(g.mode, gzip.READ)
+            with gzip.GzipFile(fileobj=f, mode='w') as g:
+                self.assertEqual(g.mode, gzip.WRITE)
+            with gzip.GzipFile(fileobj=f, mode='a') as g:
+                self.assertEqual(g.mode, gzip.WRITE)
+            with gzip.GzipFile(fileobj=f, mode='x') as g:
+                self.assertEqual(g.mode, gzip.WRITE)
+            with self.assertRaises(ValueError):
+                gzip.GzipFile(fileobj=f, mode='z')
+        for mode in "rb", "r+b":
+            with open(self.filename, mode) as f:
+                with gzip.GzipFile(fileobj=f) as g:
+                    self.assertEqual(g.mode, gzip.READ)
+        for mode in "wb", "ab", "xb":
+            if "x" in mode:
+                support.unlink(self.filename)
+            with open(self.filename, mode) as f:
+                with gzip.GzipFile(fileobj=f) as g:
+                    self.assertEqual(g.mode, gzip.WRITE)
+
     def test_bytes_filename(self):
         str_filename = self.filename
         try: