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The quality of service guaranteed multicast routing problem (QoS-MRP) is an important issue in wireless mesh networks (WMNs). However, the multicast routing is NP-complete problem. In this paper, this problem is transformed into a multi-objective combinatorial optimization problem. We present an improved discrete particle swarm optimization (PSO) approach for QoS-MRP which takes many key QoS parameters into consideration and gives a good compromise between them. The proposed algorithm was compared with SPT, KPP and an enumeration method. The simulation results show that this algorithm is effective and finds high quality solutions for QoS-MRP.