The real-time multicast problem is to construct a multicast tree starting from a source node and including multiple destination nodes and that has minimum network cost with delay constraints. It is known that to find a tree of the minimum network cost is the Steiner Tree problem which is NP-complete. In this paper, we propose a genetic algorithm to solve the multicast tree with minimum network cost and the delay constraints. The computational results obtained by comparing an existing algorithm. Kompella algorithm, and the proposed algorithm show that our algorithm tends to find lower network cost on the average than Kompella algorithm does.