diff --git a/google/cloud/bigquery/job/query.py b/google/cloud/bigquery/job/query.py
index 8049b748e..4ea5687e0 100644
--- a/google/cloud/bigquery/job/query.py
+++ b/google/cloud/bigquery/job/query.py
@@ -1532,8 +1532,9 @@ def result(  # type: ignore  # (incompatible with supertype)
         # Setting max_results should be equivalent to setting page_size with
         # regards to allowing the user to tune how many results to download
         # while we wait for the query to finish. See internal issue:
-        # 344008814.
-        if page_size is None and max_results is not None:
+        # 344008814. But if start_index is set, user is trying to access a
+        # specific page, so we don't need to set page_size. See issue #1950.
+        if page_size is None and max_results is not None and start_index is None:
             page_size = max_results
 
         # When timeout has default sentinel value ``object()``, do not pass
diff --git a/tests/unit/job/test_query.py b/tests/unit/job/test_query.py
index 5b69c98cf..4bbd31c73 100644
--- a/tests/unit/job/test_query.py
+++ b/tests/unit/job/test_query.py
@@ -1652,7 +1652,17 @@ def test_result_with_start_index(self):
 
         start_index = 1
 
-        result = job.result(start_index=start_index)
+        # Verifies that page_size isn't overwritten by max_results when
+        # start_index is not None. See
+        # https://github.com/googleapis/python-bigquery/issues/1950
+        page_size = 10
+        max_results = 100
+
+        result = job.result(
+            page_size=page_size,
+            max_results=max_results,
+            start_index=start_index,
+        )
 
         self.assertIsInstance(result, RowIterator)
         self.assertEqual(result.total_rows, 5)
@@ -1665,6 +1675,9 @@ def test_result_with_start_index(self):
         self.assertEqual(
             tabledata_list_request[1]["query_params"]["startIndex"], start_index
         )
+        self.assertEqual(
+            tabledata_list_request[1]["query_params"]["maxResults"], page_size
+        )
 
     def test_result_error(self):
         from google.cloud import exceptions