In the category of multicast routing problems, one of the most important is delay-bounded Steiner tree problem. The problem of computing such a constrained multicast tree is NPcomplete. A heuristic DBMA(Delay-Bounded Multicast routing Algorithm) to solve such a problem based on minimum delay path set and minimum cost path set is proposed in this paper. We prove that multicast trees found by this algorithm satisfy the delay constraint while the complexity is low. Simulation results further demonstrate that it is a delay constrained algorithm with low time complexity and low cost.