The key problem of QoS multicast routing optimization algorithm is to build QoS constrained multicast tree. This is the most noted problem in computer networks as constrained minimum Steiner tree problem, which has also been shown as NP-complete. A fast multicast routing optimal algorithm with QoS constraints based on Tabu-search is proposed in this paper. It chooses delay and bandwidth as QoS parameters, can improve the search speed, and make a better solution by using the merits of Tabu-search. Simulation results with random network models show that TSQMA is faster, easier for implementation, and more suitable for large group scale.