Multicast routing is the process for establishing a tree which is rooted from the source node and contains all the multicast destinations. A multicast routing tree with multiple QoS constraints is the one in which the delay, delay jitter, packet loss and bandwidth should satisfy the pre-specified bounds. This paper discusses the multicast routing problem with multiple QoS constraints, deals with the delay, delay jitter, bandwidth and packet loss metrics, and describes a network model for investigating the routing problem. It presents a multicast routing protocol with multiple QoS constraints (MRPMQ). The MRPMQ attempts to significantly reduce the overhead for constructing a multicast tree with multiple QoS constraints. In the MPRMQ, a multicast group member can join or leave a multicast session dynamically without the disruption of the multicast tree. In this paper, the proof of correctness and the complexity analysis of the MRPMQ are also given. Simulation results show that the MRPMQ is an effective approach to multicast routing decision with multiple QoS constraints.