The launch processes of a supersonic projectile in a ballistic range including separation of the sabot are numerically simulated, using moving overlapped grid method. The calculating target is a single-stage helium-gas gun, and the launch process is composed of acceleration, ventilation and sabot separation. Present numerical results correspond to experimental results both qualitatively and quantitatively regarding muzzle velocity and separation distance. The motions of the sabot and the projectile in acceleration tube can be estimated by simple one-dimensional equations. As the projectile and the sabot reach ventilation section after acceleration, high-pressure driver gas and ambient gas near the sabot are vented through small holes spread on the launch tube. After that, shock waves, which propagate at almost same velocity as the speed of the sabot, are formed forward and backward. Then, pressure difference between front surface and base surface of the sabot leads to deceleration and separation from the projectile. Furthermore, separation distance gets larger at sabot separation section. From complex flow field arisen in ventilation section and test section, the point that the sabot and the projectile separate completely should be located in sabot separation section in order to minimize the cause of flight instability.