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In recent years, QoS multicast routing has continued to be a very important research topic in the areas of networks. This paper presents a heuristic algorithm for the QoS multicast routing (HAQMR). This heuristic algorithm deals with delay and bandwidth constraints and has low cost. The HAQMR attempts to significantly reduce the overhead for constructing a multicast tree. the proof for correctness of the HAQMR is given, and the performance of the HAQMR is evaluated by simulations. The study shows that HAQMR provides an available approach to QoS multicast routing.