In order to improve the motion control accuracy of Hybrid Driven Unmanned Underwater Glider (HUG) under propulsion and glide modes, based on the theory of viscous fluids, the slip and moving body mesh techniques are used to solve the motion response equation of the HUG. The numerical prediction of the fully coupled motion response of the HUG is studied. The direct motion and circular motion of the HUG in the horizontal plane under the propulsion mode and the dive and upward movement of the HUG under the glide mode are numerically predicted. The motion response of the HUG and the effect of different center of gravity positions on the glide attitude of the HUG are analyzed under synchronous propulsion and differential rotation. The research results are of important guiding significance for the design of the structure and control system of HUG.