With the rapid development of Internet, mobile networks and high-performance networking technology, QoS multicast routing has become a very important research issue in the areas of networks and distributed systems. This is also a challenging and hard problem for the next generation Internet and high-performance networks. It attracts the interests of many people. This paper presents a distributed QoS multicast routing algorithm (DQMRA). This algorithm deals with delay and bandwidth constraints, and has low cost. The DQMRA attempts to significantly reduce the overhead for constructing a multicast tree. In this paper, the proof of correctness of the DQMRA is given, and the performance of the algorithm is evaluated using simulations. The study shows that our algorithm provides an available approach to QoS multicast routing.