In this article, we propose a three-dimensional (3D) multi-input multi-output (MIMO) channel model for air-to-ground (A2G) communications in unmanned aerial vehicles (UAV) environments, where the UAV transmitter and ground receiver are in motion in the air and on the ground, respectively. A novel angular estimation algorithm is proposed to estimate the real-time azimuth angle of departure (AAoD), elevation angle of departure (EAoD), azimuth angle of arrival (AAoA), and elevation angle of arrival (EAoA) based on the non-stationary nature of the channel model. In the model, we investigate the time-varying spatial cross-correlation functions (CCFs) and temporal auto-correlation functions (ACFs) with respect to the different moving directions and velocities of the UAV transmitter and ground receiver. Furthermore, we derive and study the Doppler power spectral densities (PSDs) and power delay profiles (PDPs) of the proposed channel model. Numerical results show that characteristics of the proposed channel model are very close to those of practical measurements, which provide a new and practical approach to evaluate the performance of next generation UAV-MIMO communication systems.