diff --git a/kombu/transport/redis_cluster.py b/kombu/transport/redis_cluster.py
index 8bc2f2373..0240643a0 100644
--- a/kombu/transport/redis_cluster.py
+++ b/kombu/transport/redis_cluster.py
@@ -202,6 +202,12 @@ def conn_or_acquire(self, client=None):
         else:
             yield self.client
 
+    def close(self):
+        for _, _, conn, _ in self.connection.cycle._chan_to_sock:
+            conn.client.close()
+
+        return super().close()
+
     def _create_client(self, asynchronous=False):
         conninfo = self.connection.client