According to their specific geometric and dynamic characteristics (small weight, huge reachable speeds ), All-Terrain Vehicles (ATVs - as quad bikes) and off-road mobile robots are very compact and driveable. They permit to realize extra agricultural tasks (spreading, spraying ) in an easier way than using once more a heavy farm tractor. However such vehicles require highly accurate control laws, able to preserve their stability even at high speed. In this paper, the prevention of off-road vehicle and mobile robot rollover are addressed by using a new active safety device. It consists in using Predictive Functional Control (PFC) so as to compute, on-line, the maximum vehicle velocity, compatible with a safe motion over some horizon of prediction, and can be applied, if needed, to the vehicle actuator to prevent from rollover. The capabilities of the proposed device are demonstrated and discussed thanks to both advanced simulations and real experimentation.