Abstract: QoS multicast routing problem is a nonlinear combinatorial optimization problem，which has been proved that the problem is NP-complete problems.This paper gives an algorithm for using the quantum evolutionary algorithm based on the principles of quantum computation to solve such problems，and improves the basic quantum evolutionary algorithm，uses evolutionary equation to adjust quantum gates and uses quantum variation to stop immature convergence in this algorithm，and makes it more suitable for QoS multicast routing solution.The simulation results show the algorithm can quickly search and convergence to the global（approximate） optimal solution，and can maintain a good characteristic as the network scale enlarges，and is superior to other evolutionary algorithm and the basic quantum evolutionary algorithm both in the optimization of speed and in the quality of solution.