This article presents vibration control of a semi-active quarter-car suspension system equipped with a magneto-rheological damper that provides the physical constraint of a damping force. In this study, model predictive control was designed to handle the constraints of control input (i.e. the limited damping force). The explicit solution of model predictive control was computed using multi-parametric programming to reduce the computational time for real-time implementation and then adopted in the semi-active suspension system. The control performance of model predictive control was compared with that of a clipped linear-quadratic optimal controller, where the damping force was bound using a standard saturation function. Two types of road conditions (bump and random excitation) were applied to the suspension system, and the vibration control performance was evaluated through both simulations and experiments.