diff --git a/google/cloud/bigquery/dbapi/connection.py b/google/cloud/bigquery/dbapi/connection.py
index 300c77dc9..459fc82aa 100644
--- a/google/cloud/bigquery/dbapi/connection.py
+++ b/google/cloud/bigquery/dbapi/connection.py
@@ -76,7 +76,8 @@ def close(self):
             self._bqstorage_client._transport.grpc_channel.close()
 
         for cursor_ in self._cursors_created:
-            cursor_.close()
+            if not cursor_._closed:
+                cursor_.close()
 
     def commit(self):
         """No-op, but for consistency raise an error if connection is closed."""
diff --git a/tests/unit/test_dbapi_connection.py b/tests/unit/test_dbapi_connection.py
index edec559b2..74da318bf 100644
--- a/tests/unit/test_dbapi_connection.py
+++ b/tests/unit/test_dbapi_connection.py
@@ -176,6 +176,22 @@ def test_close_closes_all_created_cursors(self):
         self.assertTrue(cursor_1._closed)
         self.assertTrue(cursor_2._closed)
 
+    def test_close_closes_only_open_created_cursors(self):
+        connection = self._make_one(client=self._mock_client())
+        cursor_1 = connection.cursor()
+        cursor_2 = connection.cursor()
+        self.assertFalse(cursor_1._closed)
+        self.assertFalse(cursor_2._closed)
+
+        cursor_1.close()
+        self.assertTrue(cursor_1._closed)
+        cursor_1.close = mock.MagicMock()
+
+        connection.close()
+
+        self.assertFalse(cursor_1.close.called)
+        self.assertTrue(cursor_2._closed)
+
     def test_does_not_keep_cursor_instances_alive(self):
         from google.cloud.bigquery.dbapi import Cursor