Multicasting is an important communication mechanism for implementing real-time multimedia applications, which usually require the underlying network to provide a number of quality-of-service (QoS) guarantees to users. In this paper, we study the problem concerning how to find a feasible multicast tree in which all the multicast paths satisfy the given set of QoS constraints. This problem is referred as the multiconstrained multicast tree (MCMT) problem. Based on tabu-search technique, a heuristic algorithm named MCMTS for the MCMT problem is proposed in this study. According to the experimental results, the probability of finding a feasible multicast tree by our MCMTS method is more than 99% if one exists. Furthermore, the MCMTS is also shown to be a simple and highly efficient method. As a result, it would be a practical approach for developing multicast routing protocol.