The authors formulate and propose an algorithm for the LBMT (load-balancing multicast tree) problem whose main objective is to accomplish traffic load balance while minimizing the number of multicast trees for a group. In order to fulfill these objectives, the multiple multicast tree concept, whose only disadvantage is the high tree maintenance cost, is introduced. Since the tree maintenance cost is proportional to the number of multicast trees for a multicast group, it is necessary to minimize the number of multicast trees. The authors' LBMT algorithm is based on the minimal Steiner tree approach by using the information on the available capacities of the links. For the algorithm, several link cost functions which take the available capacities on both directions into account are proposed.