In order to mitigate the adverse effect of blockages between the Unmanned Aerial Vehicle (UAV) and Ground Users (GUs), a throughput maximization algorithm for an Intelligent Reflecting Surface (IRS)-aided UAV communication network is proposed. First, considering the constraints of the energy causality, the IRS phase-shift, the UAV mobility, etc, a multi-variable coupling optimization problem is proposed with jointly optimizing the phase-shift of the IRS, the resource allocation of GUs, and the UAV trajectory. Second, the original non-convex problem is decomposed into three simpler sub-problems via the Block Coordinate Descent (BCD), which are tackled by the triangle inequality, introducing the slack variables and Successive Convex Approximation (SCA). Numerical results show that the proposed algorithm has a desirable convergence, as well as improves effectively the system sum-throughput.