Multicast routing is regarded as a critical component in networks especially the real-time applications become increasingly popular in recent years. Existing multicast routing under certain QoS Constraints tend to use conventional IP QoS architecture based on GA. In this paper, we propose a novel fast multi-objective evolutionary algorithm called QMOEA for solving multicast routing problem (MRP) in MANET. The steps are that, through the analysis of the strengths and limitations of the well-known multicast architecture, we firstly give an improved Core Based Tree model to simplify the MRP. Based on this model, we then propose the QMOEA which integrates the "Greedy" and "family competition" approaches to speed up the convergence and to maintain the diversity of population. After that, we present the theoretical validations for the proposed method to show its efficiency, and finally, the performance of MANET scaled from 20 to 200 nodes with different types of service is evaluated by OPNET, our experimental results show that our proposed method is capable of achieving faster convergence and more preferable for multicast routing in MANET compared with other genetic algorithms (GAs) well-known in the literature.