The combined input-crosspoint-queued (CICQ) crossbar switch is very appealing because it can obtain high throughput with simple scheduling mechanisms. However, in order to support multiple priority levels, separate queues per priority are required at each crosspoint, hence there needs much more memories and many priority schedulers to be implemented in a buffered crossbar, which is of great complexity. In this paper we propose a scheme that uses a hierarchical priority queuing mechanism in the input queues and a simple queue per crosspoint to effectively support multiple priorities. We present a priority weighted double round robin (PWDRR) scheduling algorithm in input scheduler to implement bandwidth allocation among multiple priorities and a simple compensation priority round robin (CPRR) scheduling policy in crosspoint scheduler to transfer cells to the output. The simulation results verify a preferable performance of our scheme.