QoS (quality of service) multicast routing is essential to NGI (next generation Internet). On one hand, due to difficulty in exact measurement and expression of NGI network status, the necessary QoS routing information should be fuzzy. On the other hand, with the gradual commercialization of network operation, paying for network usage calls for QoS pricing and accounting. However, benefit conflicts between network providers and users ask the so-called both-win to be supported. Thus, a fuzzy integral and game theory based QoS multicast routing scheme is proposed and has been implemented by simulation. It consists of three parts: Edge evaluation, game analysis, and multicast tree construction. It does comprehensive evaluation on candidate edges based on fuzzy integral and adaptability membership degree functions for edge parameters, determines whether Nash equilibrium between network provider utility and user utility has been achieved on candidate edges by gaming analysis, and attempts to construct a multicast routing tree with not only user QoS requirements satisfied but also Pareto optimum under Nash equilibrium on network provider utility and user utility achieved or approached by the proposed algorithm. Simulation results show that performance of the proposed scheme is better than that of some well known schemes, including QoSMIC.