In order to study the dynamics modeling and stability control design of supercavitating vehicle at the acceleration stage, the shape of natural cavity and the deviation of its axis were investigated according to the principle of cavity expansion independence. The influences of the cavity memory effect, gravity, cavitator orientation effect and attack angle were considered. The hydrodynamic force on each region of the supercavitating vehicle was calculated by means of the theory of slender bodies. Then a mathematical model for the acceleration stage of the supercavitating vehicle was presented for the longitudinal plane. Based on the precision linearization method, a depth tracking controller was designed. The simulation results show that this controller has better tracking performance; the planing force goes to zero in a short time, so the stability of the vehicle is improved and the friction drag of the partially wetted region is decreased.