This study deals with the topology discovery for the capacitated minimum spanning tree network. The problem is composed of finding the best way to link nodes to a source node and, in graph-theoretical terms, it is to determine a minimal spanning tree with a capacity constraint. In this paper, a heuristic algorithm with two phases is presented. Computational complexity analysis and simulation confirm that our algorithm produces better results than the previous other algorithms in short running time. The algorithm can be applied to find the least cost multicast trees in the local computer network.