Traditional underwater vehicles are limited in speed due to dramatic friction drag on the hull. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase their underwater speed. Compared with fully wetted vehicles, the non-linearity in the modelling of cavitator, fin and in particular the planing force make the control design of supercavitating vehicles more challenging. Dominant non-linearities associated with planing force are taken into account in the model of supercavitating vehicles in this paper. Two controllers are proposed to realize stable system dynamics and tracking responses, a linear quadratic regulator (LQR) control scheme and a robust backstepping control (RBC) scheme. The proposed backstepping procedure, in association with integral filters technique, exploits the possibility of avoiding the overparameterization problem existing in the classical backstepping process. In particular, the achieved stability is robust to modelling errors in supercavitating vehicles. Compared with the LQR control scheme, the RBC scheme is seen to increase the robustness with saturation compensation algorithm, which can be useful for avoiding actuator saturation in magnitude.