In this letter, we present a novel intelligent reflecting surface (IRS)-assisted unmanned aerial vehicle (UAV) communication system, where both the IRS and ground users (GUs) can achieve self-sustainable operations by exploiting the energy harvesting (EH) technique. We consider a practical scenario that the direct links between the UAV and GUs always suffer from blockages, typically in complex urban scene. To mitigate this adverse effect, the IRS can be properly deployed to create a clear propagation environment. We maximize the sum-rate for the proposed system by jointly optimizing the IRS's phase-shift, transmit power and time allocation of GUs, and trajectory of the UAV. To handle the non-convexity caused by coupled variables, the original problem is decomposed into three subproblems and solved by the block coordinate descent (BCD) method. Through numerical results, the proposed algorithm can achieve significant performance gains over the benchmarks.