In cognitive wireless Mesh networks, the multiple-objective optimization problem with quality of service constraints is more complicated than the single objective optimization problem. To obtain the optimal multicast routing solution which satisfies the quality of service constraints and is aimed at minimizing the channel collision and the resource consumption, a problem solving framework which contains problem description, particle encoding, particle initialization, fitness function, particle flight, particle mutation, particle elimination circle, was proposed on the basis of particle swarm optimization. Adjacency matrix which shows the connection relation between nodes was used to represent particle. Three operation rules, particle flight operation and particle mutation operation were redefined. Simulation results show that the proposed algorithm can achieve the expected goal. It can achieve the effect of a lower resource consumption and a smaller channel collision value.