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As a NP-complete problem, multicast routing with delay and delay variation constraints is a research difficulty in multicast communications. In this paper, we propose an efficient multicast routing algorithm based on simulated annealing named SADDVMA to construct delay and delay variation constrained Steiner tree. The proposed algorithm uses a procedure called Paths Switching to construct neighbors in feasible region, which greatly reduces the search area and computing time. Simulations demonstrate that our algorithm is better in terms of tree cost as compared to the existing algorithms. Further, it performs excellent performance of delay and delay variation, high success ratio, rapid convergence and better real-time property.