Low-Cost Shortest Path Tree is a commonly-used multicast tree type, which can minimize the end-to-end delay and at the same time reduce the bandwidth requirement if possible. Based on the low-cost shortest path tree algorithm DDSP (destination-driven shortest path) and through improving on the search procedure, a Fast Low-cost Shortest Path Tree (FLSPT) algorithm is presented in this paper. The Shortest Path Tree constructed by the FLSPT algorithm is the same as that constructed by the DDSP algorithm, but its computation complexity is lower than that of the DDSP algorithm. The simulation results with random network models show that FLSPT algorithm is more effective.