本文针对MPH(MinimumPathCostHeuristic)等多播最小生成树算法存在的问题 ,通过改进最短路径节点的搜寻过程 ,以较小的存储空间为代价 ,获得了计算效率很高的快速最小代价多播生成树算法FMPH(FastMinimumPathCostHeuristic) ,且获得多播生成树与MPH算法完全相同 .随机网络模型的仿真结果表明 :FMPH算法快速、稳定 ,是一种值得推广使用的高效算法 . Aiming at the problem of minimum spanning tree algorithm such as MPH (Minimum PathCostHeuristic) and so on, by improving the searching process of the shortest path node, a fast and minimum cost multicast spanning tree algorithm with high computational efficiency is obtained at the cost of small storage space FMPH (FastMinimumPathCostHeuristic), and obtains the multicast spanning tree exactly the same with the MPH algorithm.The simulation results of the stochastic network model show that the FMPH algorithm is fast and stable, and is an efficient algorithm worthy of promotion.