diff --git a/googleapiclient/http.py b/googleapiclient/http.py
index 1b661e1..927464e 100644
--- a/googleapiclient/http.py
+++ b/googleapiclient/http.py
@@ -733,7 +733,7 @@
         headers = self._headers.copy()
         headers["range"] = "bytes=%d-%d" % (
             self._progress,
-            self._progress + self._chunksize,
+            self._progress + self._chunksize - 1,
         )
         http = self._request.http
 
diff --git a/tests/test_http.py b/tests/test_http.py
index 852cd7e..e55e056 100644
--- a/tests/test_http.py
+++ b/tests/test_http.py
@@ -488,6 +488,23 @@
         self.assertEqual(5, download._progress)
         self.assertEqual(5, download._total_size)
 
+    def test_media_io_base_download_range_request_header(self):
+        self.request.http = HttpMockSequence(
+            [
+                (
+                    {"status": "200", "content-range": "0-2/5"},
+                    "echo_request_headers_as_json",
+                ),
+            ]
+        )
+
+        download = MediaIoBaseDownload(fd=self.fd, request=self.request, chunksize=3)
+
+        status, done = download.next_chunk()
+        result = json.loads(self.fd.getvalue().decode("utf-8"))
+
+        self.assertEqual(result.get("range"), "bytes=0-2")
+
     def test_media_io_base_download_custom_request_headers(self):
         self.request.http = HttpMockSequence(
             [