Application Layer Multicast (ALM) is more flexible than that in IP layer and easy to optimize for specific applications, so the research on it has become a hotspot. Aiming at the problem of most ALM protocol ignoring bandwidth of covering tree, the paper presented a new heuristic algorithm Max-Delta, which inferred the underlying link topology using end-to-end measurement technology. On the basis of this, a kind of Fast Application layer Tree (FAT) algorithm to construct covering tree was proposed to meet the requirements of bandwidth. In addition, the algorithm's time complexity was also analyzed. Simulation results show that Max-Delta algorithm can obtain network topology accurately with less network measurement times comparing with random measurement algorithm and longest path measurement algorithm.