Abstract: The continuous demand for using multimedia applications over the Internet has triggered a spur of research on how to satisfy the quality of service （QoS） requirements of these applications. These efforts resulted in the proposals of several QoS-based frameworks. At present,multicast communications among multiple hosts in networks usually require multiple strict quality of service guarantees. In this paper,a selection process of determining multicast routes satisfying the different QoS constraints is converted into a multiobjective optimization problem. Then a novel multicast tree computation algorithm is provided,which optimizes several QoS parameters on delay,loss ratio and bandwidth utilization simultaneously. Simulation results show that this algorithm is effectively capable of obtaining a set of non-dominated multicast routes within a finite evolutionary generation,which takes advantage of multiobjective optimization and overcomes the weakness of multicast routing with a single objective.