This paper investigates an unmanned aerial vehicle (UAV)-aided wireless powered communication network where a mobile hybrid access point serves multiple energy-constrained ground terminals (GTs) in terms of wireless energy transfer and data collection. Specifically, to support information transmission of the GTs, the mobile UAV first transfers wireless energy in the downlink. Then, by harvesting this wireless energy, the GTs transmit their uplink information signals to the UAV in a time division multiple access manner. In this system, we jointly optimize the trajectory of the UAV and the uplink power control policy in order to maximize the minimum throughput of the GTs. By applying the concave-convex procedure, we propose an iterative algorithm which efficiently identifies a locally optimal solution. Simulation results verify the efficiency of the proposed algorithm compared to conventional schemes.