To support different QoS requirements in terms of bandwidth and delay constraints imposed by heterogeneous and dynamic joining receivers, this paper proposes an algorithm named QDMR-LD (QoS-based dynamic multicast routing for streaming layered data). When a new receiver joins, receiver-oriented path searching heuristic is used to find a feasible path with minimum cost from the multicast tree to the receiver. RBMF (reverse best metric forwarding) mode proposed in our previous work is adopted in this paper to increase the joining success ratio. When a receiver leaves, corresponding part of the multicast tree is pruned. Simulation results show that QDMR-LD increases the success ratio and lowers the multicast tree cost compared with other related schemes.