In this paper, an active steering control strategy is proposed to prevent rollover of a vehicle with a time-varying forward speed. The controller is designed with the aim of reducing the rollover index (RI) from an initial dangerous status to an absolutely safe status by active steering. The controller consists of two parts. The nominal control is firstly designed on the basis of the fundamental equation of constrained motion (FECM) of the vehicle, which will guarantee the nominal vehicle to track the desired states and thus rollover is prevented. To handle system uncertainties, compensatory sliding mode control (SMC) is proposed, by which the actual states are forced to track the desired ones. In the controller, the chattering problem can be alleviated by selecting a suitable performance function. To indicate the merits of the designed controller, simulation is conducted. Simulation results demonstrate that compared to conventional controllers, the proposed controller can prevent the vehicle from rollover with stronger robustness and without system chattering.