Delay and stability are two key factors that affect the performance of multicast data transmission in a network. However, current algorithms of tree generation hardly meet the requirements of low delay and high stability simultaneously. Given a general network, the generation algorithm of a multicast tree with minimum delay and maximum stability is an NPhard problem, without a precise and efficient algorithm. To address these challenges, this paper studies the generation of low-delay and high-stability multicast trees under the model of spanning tree based on stability probability, degree-constrained, edge-weighted for multicast (T-SDE). A class of algorithms was proposed which creates the multicast tree greedy on the ratio of fan-out to delay (RFD) and probability of stability of terminal to obtain a high performance in multicast. The proposed algorithms greedily select terminals with a large RFD and a high probability of stability as forwarding nodes in the generation of the multicast tree, where the larger RFD and higher stability of upstream nodes are beneficial to achieve a low transmission delay and high stability in multicast. The proposed RFD can be compatible with the original model, which can take advantage of network connectivity during the generation of a multicast tree. This paper carries out simulation experiments on Matlab R2016b to measure the performance of the proposed algorithm. Experimental results show that the proposed algorithm can provide a smaller height, higher stability, and a lower transmission delay of the resulting multicast tree than other solutions. The spanning tree of the proposed algorithms can support low transmission delay and high stability in multicast transmission.