This paper proposes a control strategy dedicated to trajectory tracking of off-road mobile moving at high speed. In order to account for bad grip conditions and high dynamics encountered in this context, an adaptive and predictive approach is detailed, based on several models (kinematic and dynamic). This permits to obtain a high accuracy level in motion control, while preserving the robot stability with respect to the rollover risk when moving fast. The capabilities of the proposed algorithm are investigated on an actual mobile robot acting on natural ground.