A dispatching algorithm is always indispensable research topic for a switching system. In studying the future-generation high-speed switching and routing system, a concurrent round-robin dispatching algorithm with active grants, called CRRD-AG, is proposed in this paper. As a multistage switching architecture, Clos-network has been receiving increasing attention due to its scalability and modularity, and yet it is not much that the corresponding dispatching algorithm can be applied to the multistage switching fabric. So far, some well-known dispatching algorithms, such as concurrent dispatching (CD) and concurrent round-robin dispatching (CRRD), either have low throughput or can not handle various traffic. CRRD-AG algorithm based on CRRD improves the typical request- grant-accept (R-G-A) matching model used by CRRD to the active grant-accept (AG-A) matching model. Consequently, not only the iterative messages of the request phase can be reduced significantly, but also the bandwidth of the central stage can be utilized sufficiently. Therefore, the average delay is decreased and the throughput is increased. Also, simulations show that CRRD-AG achieves 100% throughput under uniform traffic and bursty traffic. More importantly, the average delay performance of the whole switching system is improved significantly without reducing the throughput of the switching system.