With the rapid development of communication networks, the quality of service (QoS) on such networks has become an important research topic. With regard to ad hoc networks, this paper presents an evolutionary algorithm (EA) and an ant colony algorithm (ACA) to serve as the basis for a QoS multicast routing algorithm (EA-ACA-QMRA). This algorithm combines the rapid global search capability and robustness of EAs with the pheromone feedback factors of ACAs while accounting for multiple constraints, including constraints related to delay, delay jitter, packet delivery ratio, bandwidth and cost. For the case of self-adapting ad hoc networks in particular, our new algorithm is far superior to traditional ACAs. Our experimental results show that the EA-ACA-QMRA can address multiple constraints in the QoS multicast routing problem and can achieve higher accuracy and faster convergence than can traditional ACAs in terms of the end-to-end delay and packet delivery ratio. The proposed algorithm provides an effective means of solving the QoS multicast routing problem for ad hoc networks, and it is better than the traditional methods at avoiding network congestion.