Wireless mesh network is a new broad bandwidth distributing wireless access network system. It can access Internet through gateway nodes. When network load of access is heavy or network size is expanding, one gateway node will become a bottleneck of the access network because of the serious congestion of a large number of data packets transmitted to the gateway node. Based on the research of DSR (dynamic source routing protocol) and anycast service, a multi-gateway wireless mesh network routing protocol(MAMSR) was presented. In this protocol, the anycast group members were multiple gateways, and DSR was expanded to support anycast. Simulation results show MAMSR can effectively solve the congestion of single gateway, maintain high packet mailing rate, low delay and routing cost, and make the access network run stably and efficiently.