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The advent of various real-time multimedia applications in high-speed networks prompt the necessity of quality of service (QoS) based multicast routing and the constrained Steiner tree as the mathematical structure behind it which is a wellknown NP-complete problem. Two important QoS constraints are the bandwidth constraint and the end-to-end delay constraint. In this paper, an algorithm is proposed to solve the bandwidth-delayconstrained least-cost multicast routing problem based on Tabu Search (TS). Computational results for various random generated networks show that the proposed algorithm outperforms other existing TS-based algorithms and heuristics.