As a new technology for reconstructing communication environments, intelligent reflecting surfaces (IRSs) can be applied to UAV communication systems. However, some challenges exist in IRS-assisted UAV communication system design, such as physical layer security issues, IRS design, and power consumption issues owing to the limitation of the hardware. Therefore, a secrecy capacity optimization scheme for an active IRS-assisted unmanned aerial vehicle (UAV) communication system is proposed to solve multi-user security issues. In particular, controllable power amplifiers are integrated into reflecting units to solve the problem of blocked links, and the UAV can dynamically select the served user according to the channel quality. In order to maximize the system average achievable secrecy capacity and ensure the power constraints of the UAV and active IRS, user scheduling, UAV trajectory, beamforming vector, and reflection matrix are jointly optimized, and the block coordinate descent (BCD) algorithm is applied to solve this non-convex problem. Simulation results show that the active IRS-assisted UAV communication scheme can significantly weaken the “multiplicative fading” effect and enhance the system secrecy capacity by 55.4% and 11.9% compared with the schemes with passive IRS and without optimal trajectory, respectively.