Underwater gliders are recent innovative types of autonomous underwater vehicles (AUVs) used in ocean exploration and observation. They adjust their buoyancy to dive and to return to the ocean surface. During the change of altitude, they use the hydrodynamic forces developed by their wings to move forward. Their flights are controlled by changing the position of their centers of gravity and their buoyancy to adjust their trim and heel angles. For better flight control, the understanding of the hydrodynamic behavior and the flight mechanics of the underwater glider is necessary. A 6-DOF motion simulator is coupled with an unsteady potential flow model for this purpose. In some specific cases, the numerical study demonstrates that an inappropriate stabilizer dimension can cause counter-steering behavior. The simulator can be used to improve the automatic flight control. It can also be used for the hydrodynamic design optimization of the devices.