Multicast routing in multirate mesh network wireless networks is challenging, mainly due to multirate transmissions and quality of services guarantee. In this paper, we present a self-learning multicast routing algorithm for multirate WiFi (Wireless Fidelity) mesh network. First, we design a self predict routing information mechanism to predict the delay and bandwidth of every multicast tree. The trees which delay and bandwidth can meet the multimedia service needs will be chosen into the metric compare procedure. Then, we introduce the time slot, bandwidth and transmit rate into the new metric function. Moreover, a real-time automatic monitor is implemented to guarantee the delay in the time varying wireless channel. The proposed algorithm runs in the same running time as regular shortest-path algorithms and bandwidth-constraint algorithms. The experiments results show that self-learning multicast routing algorithm is capable of establishing a route which has higher time slot efficient and network performance with delay and bandwidth constraint.