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With the rapid development of high-performance networking technology, multicast routing with quality of service (QoS) constraints has continued to be a very important research issue in the fields of the networks and distributed systems. This paper discusses the multicast routing problem with QoS constraints such as delay, delay jitter, bandwidth and packet loss metrics, and describes a network model that is suitable to search such routing problem. The paper mainly presents a QoS-guaranteed multicast routing protocol (QGMRP). The QGMRP can operate on top of the unicast routing protocol. The QGMRP can significantly reduce the overhead for constructing a multicast tree with QoS constraints. In QGMRP, a multicast group member can join or leave the multicast session dynamically. The protocol can search multiple feasible tree branches, and select the optimal or near-optimal branch for connecting the new receiver to the multicast tree if it exists. In this paper, the proof of correctness and complexity analysis of the QGMRP are given, and the performance measures of the protocol are evaluated using simulation. The study shows that QGMRP provides an available approach to multicast routing with QoS constraints.