The integration of unmanned aerial vehicles (UAVs) and terahertz (THz) technology can provide high data rate for air-to-ground (A2G) communications. In this paper, a non-stationary geometric sub-THz multiple-input multiple-output (MIMO) channel model is proposed for UAV A2G communication based on a three-dimensional (3D) semi-spherical model. The detailed channel modeling of reflection fading and scattering fading on the rough surface in sub-THz band is considered. According to the proposed geometry-based stochastic model (GBSM), the space-time correlation function (STCF) has been derived and the impact of several important UAV-related parameters on the STCF has been investigated and compared to the millimeter-wave (mm-wave) bands. The results indicate that the stationary time separation of channel and the dependency of spatial cross-correlation function (S-CCF) on antenna element spacing in sub-THz band of 140GHz are both smaller than those in mm-wave band of 28GHz.