Focusing on the problem of high computational complexity of weighted arbitration scheme for Combined Input and Crosspoint Queued(CICQ) switches, a new scheduling algorithm called Long Queue Prioritized-Round Robin (LQP-RR) was proposed. By using the local variation feature of virtual output queues, the complex sorting operation at input scheduling was simplified. In addition, a secondary pointer was adopted to guarantee the fairness of the algorithm. The new algorithm only need one time compare operation at input port, which indicates that the algorithm has a low complexity and is easy to implement. Theoretical analysis illustrated that the proposed algorithm can achieve 100% throughput for any admissible traffic that satisfies the strong law of large numbers. Finally, simulation showed that LQP-RR exhibits good delay and throughput performance under any admissible traffic.