This paper proposes an algorithm dedicated to off-road mobile robot path tracking at high speed. In order to ensure a high accuracy, a predictive and adaptive approach is developed to face the various perturbations due to this context (mainly the bad grip conditions and the terrain geometry). The control law is based on previous work, and requires the knowledge of sideslip angles, which cannot be directly measured. As a result, an observer based on two levels of modeling (kinematic and dynamic) is proposed to ensure a relevant and fast estimation. If the kinematic part is independent from the terrain geometry, the dynamic model used in this paper requires to take explicitly into account the influence of the terrain geometry on mobile robot dynamic. It is achieved by the introduction of the lateral robot inclination, which is on-line estimated via a kalman filter and integrated in the dynamical model. The advantages of the proposed contribution to path tracking control are investigated through full-scale experiments achieved at high speed (up to 6m/s) on an uneven and grass field.