This paper investigates topological designs for multicast networks using simulated annealing (SA) and proposes a new method for finding an effective initial solution to the problem of reducing the computational time of SA. Multicast communications can decrease network traffic due to branch connections. Accordingly, multicast services will be predominant in future traffic. Since the characteristics of multicast communications are quite different from those of unicast communications, it is necessary to find a suitable topology for future networks that accommodates both multicast and unicast services. Finding the optimal topology is generally known as an NP-hard problem, and so heuristic algorithms have been used in many cases. This paper optimizes the multicast network topology by simulated annealing, a well-known powerful heuristic. Even if SA were employed, however, more additional inventions would be required to compute and find the solution with the smallest possible number of iterations. Therefore, this paper proposes a method for finding an effective initial solution for SA. The results show that the computational time needed to reach the final solution becomes shorter if our proposed method is applied.