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Geometry-based stochastic modeling (GBSM) for UAV air-to-ground (A2G) channel usually assumes fixed velocity and moving direction, which can't describe the non-stationary characteristics of the UAV air-ground propagation environment. Facing the UAV 3D air-to-ground channel model based on double cylindrical scatterer, this paper proposed to introduce a Gauss Markov mod el with dynamic speed and moving direction into the A2G to simulate the changes of the UAV in the real environment. In order to make the model simulate different motions, it introduced an expansion factor to switch the motion trajectory of the model. In addition, this paper used the geometric analysis method to derive the space-time correlation function and Doppler power spectral density based on the time-varying speed and direction of motion, and studied the influence of the UAV horizontal and vertical movement on the channel statistical characteristics. The simulation results show that the extended model only cause non-stationarity in the time domain without affecting the air space, and verifies the generality of the extended model. [ABSTRACT FROM AUTHOR]