Abstract: QoS-based multicast routing algorithms are required to satisfy the QoS requirements of each individual application and to manage network resource efficiently. A new heuristic algorithm is presented for constructing low-cost multicast tree with end-to-end delay constraints. It first constructs a constrained low-cost multicast tree using a modified Steiner tree heuristic, and then connects the rest group members which are not on the constrained multicast tree using least delay paths. The simulation results show that its per formance compares well with other known delayconstrained heuristics. Moreover, the algorithm does not suffer from high complexity common to most delay-constrained heuristics.