The research works carried out in this paper deal with the control of a fast double-steering off-road mobile robot. Such kind of robots requires very high stable and accurate controllers because their mobility is particularly influenced by wheel–ground interactions. Hence, the vehicle dynamics should be incorporated in the control circuit to take into account these issues, which is developed based on the road geometry parameters and the slippage-friction conditions at the wheel–ground contacts. Relying on this dynamic model, we present in this paper the design and application of a constrained Model Predictive Control (MPC). It is based on the minimization of a cost function (optimizing the deviation from the reference trajectory, and the variation of the control input) along a finite prediction horizon, however, the prediction horizon is variable according to the forward speed of the robot. On the other hand, this approach incorporates several constraints, essentially important for the stability and safety of an off-road mobile robot moving at the high velocity, namely : saturation and maximum variations of the vehicle’s actuators (i.e. steering joints and their speeds limits) as well as the tire adhesion zone bounds (allowing to validate the assumption of a linear tire model). The full optimization problem is formulated as a Linearly Constrained Quadratic Programming (QP) to compute at each time-step the optimal and dynamically-consistent front and rear steering angles that are required to reach the desired path, with respect to all these constraints. The capabilities of our proposed controller are compared with another control law which does not apply any physical or intrinsic constraints. The latter is simply a feedback controller based on the same dynamic model and LQR theory (Linear Quadratic Regulator). Both of them have been investigated through several tests on simulations via ROS/GAZEBO and experiments on a real off-road vehicle for different kinds of trajectories and velocity levels.