Traditional unmanned aerial vehicle (UAV) air-to-ground channel models cannot support three-dimensional (3D) flight trajectories and 3D antenna arrays. In this paper, by introducing the spatial rotation matrix and trajectory parameters, a modified 3D geometry-based stochastic channel model for UAV-based air-ground links is proposed. Considering UAV air-to-ground communication scenarios, the proposed model adopts the time-varying Boolean variables to describe the dynamic birth and death processes of line-of-sight path, ground reflection path and other scattering paths. Meanwhile, the corresponding time-evolving algorithms of channel parameters, i.e., two-dimensional angle, delay and power, are given and analyzed. The upgraded method can be used to reproduce the time-variant statistical properties of UAV air-to-ground channels. The numerical simulation results have demonstrated that the output spatial-temporal correlation characteristics and Doppler power spectrum of our model are consistent well with the theoretical ones, and the auto-correlation characteristic agree well with the measured one. The proposed model is helpful for communication system optimization, algorithm verification and performance evaluation of UAV-based wireless communication equipment.