Intelligent reflecting surface (IRS) composed of a large number of low-cost passive reflecting elements has attracted significant attention from communication communities because of its ability to substantially improve the communication performance. In this paper, the aperture area and radiation pattern of the IRS reflecting elements are considered, and a novel geometry-based three-dimensional (3-D) wideband channel model is proposed for IRS-assisted unmanned aerial vehicle (UAV) communication systems. In the proposed model, the reflection phase is designed by jointly considering the aperture area of the IRS reflecting element and the propagation phases among UAV, IRS, and receiver (Rx), each IRS reflecting element is modeled as an anomalous reflector instead of a specular reflector, and large-scale IRS reflecting elements can jointly beamform the signal in a desired direction. Based on the proposed model, the effects of arbitrary trajectory of UAV and the number and the size of passive reflecting elements on channel statistical characteristics are considered, and the average received signal power and the ergodic sum capacity, which consider the impacts of the number and the size of passive reflecting elements, are also investigated. Furthermore, the path loss of the IRS-assisted link, which is in inverse proportion to the square of aperture area of IRS reflecting elements, is derived, and it coincides with the measured results in real outdoor scenarios. Analysis shows that the communication performance can be enhanced by increasing the number and the size of IRS reflecting elements, and it is validated by numerical results and Monte-Carlo simulation results.