In this paper, we consider a multiuser downlink communication system, where ground users are served by a UAV base station flying on an aerial plane. For the sake of computational complexity and energy economy, we propose a polygonal-line trajectory for the UAV base station and each ground user is served one by one while the UAV base station is travelling along one of the line segments on the trajectory. With the polygonal- line trajectory, joint optimization for power control and trajectory design for the UAV base station is investigated to maximize total capacity of all the ground users. Such a problem is decomposed into three subproblems for single-user downlink power profile, transmission energy allocation and waypoints location selection, respectively, and solved via alternate optimization, with which one of the three subproblems is solved given solutions to the other two. Simulation results show that the proposed scheme with optimized power profile and trajectory for the UAV base station outperforms two baselines. We also show that trajectory design significantly impact the system performance and is indispensable in UAV-assisted communications.