Real time transmission, which is delay sensitive, is an important aspect of application-layer multicast. It is crucial to build an efficient multicast tree to guarantee the lower delay. This research is focused on the algorithms of the minimum-delay spanning tree for the application-layer multicast. Firstly, it is stated that the total delay is affected by communication delay, processing delay and the degree of nodes. Then the network is modeled into the node-and-edge-weighted directed graph with the limited degree of nodes. In this model the problem is shown to be NP-hard. Therefore, two kinds of heuristic algorithms are proposed, which are based on the maximum degree and the maximal length path respectively. Finally, the simulation demonstrates that the proposed algorithms are valid.