Recently, unmanned aerial vehicles (UAVs) have been widely studied in the communication area to work as aerial base stations, due to the high probability of line of sight (LoS) and high flexibility. However, few works consider fairness for the users, which is one of the most important metrics for a network. In this paper, in order to maximize network capacity with the consideration of fairness, trajectory and scheduling of the mobile UAV aerial base station are jointly optimized. Firstly, the problem of maximizing network capacity with the consideration of fairness is formulated. On account of the coupling relationship of trajectory and scheduling, an alternate iteration approach that contains ant colony algorithm and genetic algorithm are then proposed to solve this intractable problem. Finally, the simulation results demonstrate the fairness enhance of the network and the validity and effectiveness of the proposed optimization approach.