As multicast transmission is gaining importance in the wireless network setting, the NP-complete nature of the optimum wireless multicast tree problem makes it necessary to develop efficient and computable heuristics. In this paper, we present a new distributed routing algorithm. The length of the multicast tree computed by the algorithm (more precisely, the number of transmissions needed to reach all multicast nodes) as a function of the number of nodes, N, and the size of the multicast group, M, is very close to a lower bound provided in the literature, while the computational complexity is at most O(N3). Moreover, the number of messages that need to be exchanged to establish the tree is reasonable. A repair and maintenance algorithm has also been suggested for adaptation to topology changes, which tend to occur in practical applications.