Underwater Glider (UG) is a new type of underwater vehicle which has been introduced decades. Compared with the other underwater vehicles (UV), it has obvious advantages, such as small noise and strong concealment, and the function of autonomous underwater navigation. This thesis focused on the design and the vertical motion of the UG. Also the effects of the movable mass and the buoyancy engine on the gliding parameters are important issues. In order to decrease the resistance of the glider in the water, the Myring hull profile equation was designed for the streamlined cockpit, and the posture balance analysis of the UG was analyzed using Solidworks. The motion equations of the UG in the vertical plane were derived and established. The computer simulation of the UG was performed using Simulink in Matlab to analyze the influence of the movable mass and the buoyancy engine on the gliding state. The computational fluid dynamics(CFD) technique was used for analyzing the hydrodynamics of the glider, where empirical parameters of the hydrodynamic force are obtained by data fitting.