Abstract: The current practical scheduling algorithms supporting unicast and multicast traffic in high-speed crossbars are generally based on a request-grant-accept process, such as ESLIP. But there is a phenomenon called Grant blocking between unicast and multicast cells in this kind of algorithms, which decreases the scheduling efficiency. According to the practicability, this paper presents a new algorithm supporting unicast and multicast trafficERGRR (Extended Request-Grant-based Round-Robin). ERGRR overcomes the Grant blocking and improves the system performance, such as throughput and delay, by simplifying execution process. The simulation results show that the ERGRR can achieve better performance of throughput and delay than ESLIP under various unicast and multicast traffics. In addition, ERGRR provides better fairness and its implementation complexity is lower than ESLIP.