Driven by the rapidly growing demand for information security, covert wireless communication has become an essential technology and attracted tremendous attention. However, traditional wireless covert communication is continuously exposing the inherent limitations, creating challenges around deployment in environments with a large number of obstacles, such as cities with high-rise buildings. In this paper, we propose an intelligent reflecting surface (IRS)-assisted covert communication system (CCS) for communicating with a friendly unmanned aerial vehicle (UAV) in which the UAV generates artificial noise (AN) to interfere with monitoring. Furthermore, we model the power of AN emitted by the UAV using an uncertainty model, through which the closed-form detection error probability (DEP) of the covert wireless communication for monitoring is derived. Under the derived DEP, we formulate the optimization problem to maximize the covert rate, then design an iterative algorithm to solve the optimization problem and obtain the optimal covert rate using Dinkelbach method. Simulation results show that the proposed system achieves the maximum covert rate when the phase of the IRS units and the trajectory and transmit power of the UAV are optimized jointly.