As the mobile networks become even denser and the traffic demand is increasing drastically, it is becoming more heterogeneous. Recently, it is intensive to investigate the Cell-Free Massive multiple-input multiple-output Massive (MIMO) system, where a large number of access points (APs) simultaneously serve a much smaller number of users, and the APs and users are clustered to provide good service for all users. This paper designs a mobile base station (MBS)-assisted Cell-Free Massive MIMO system: Utilizing an MBS deployed on the unmanned aerial vehicle (UAV) to form an air-ground heterogeneous system with the Cell-Free Massive MIMO system and offload part of traffic to the MBS to further improve the system performance. To provide better service to all users, this paper design an MBS flight trajectory optimal method to improve the wireless coverage performance and user experience, and proposed a joint power allocation algorithm based on the consideration of the fairness of the service quality. The simulation results indicate that the performance of the system designed in this paper has a significant improvement compared with the normal Cell-Free Massive MIMO system.