The research on wireless mobile Ad hoc networks has attracted much attention over the past few years, and IP multicast technology supports data transmission from one or several sources to a certain group of receivers. PUMA, as a mesh-based multicast routing algorithm for Ad hoc networks, has been demonstrated to perform better compared with other protocols under high-speed situation. Moreover, node mobility has been one of the dominant factors causing loss of system performance so that the stability is necessary to be taken into account when designing routing protocols. In this paper, a novel stability-based multicast routing algorithm (SMRA) is developed on the basis of PUMA, where the robustness and the congestion are jointly considered. In order to determine the forwarding path and the mesh member status of each node, SMRA utilizes the power information and is implemented across physical layer and network layer. We compare SMRA with PUMA and another well-known tree-based multicast protocol MAODV. Simulation results show that the performance of the proposed algorithm is better than that of PUMA and MAODV in terms of packet delivery ratio and throughput with limited control overhead.