Driven by the rapidly growing demand for information security, covert wireless communication conceived as one of the essential technology has attracted tremendous attention. However, traditional wireless covert communication is continuously exposing the inherent limitations that challenge deploying 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) with a friendly UAV, where the UAV generates artificial noise (AN) to interfere with the monitors. Furthermore, we model the power of AN emitted by UAV as an uncertainty model, with which the closed-form detection error probability (DEP) on the covert wireless communication for the monitor is derived. Under the derived DEP, we formulate the optimization problem to maximize the covert rate, and an iterative algorithm is designed to solve the optimization problem to obtain the optimal covert rate by using Dinkelbach method. Simulation results show that the proposed system achieves the maximum covert rate when the phase of the IRS units, the trajectory, and the transmit power of the UAV are jointly optimized.