This paper proposes a model predictive control (MPC) scheme based on linear parameter variation to enhance the damping control of speed-dependent active suspensions. The controller is developed by introducing a speed-dependent term, specifically front- and rear-wheel time delays, to the half-car model using the Padé approximation. Subsequently, the model is augmented with time-varying parameter dependence. An adaptive Kalman filter based on variance matching is employed to estimate system states affected by imprecise sensor measurement noise. Finally, a set of explicit control laws incorporating road preview information and available vehicle speed are determined offline using multi-parameter linear programming (mp-LP), simplifying online implementation to searching for optimal solutions in a lookup table. Simulation results demonstrate a significant improvement in active suspension control under changing vehicle speeds compared to passive control.