Multiplexed model predictive control (MMPC) is a recently proposed efficient model predictive control (MPC) algorithm, which can effectively reduce the computational burden of the online optimisation in MPC implementation by updating the control inputs in an asynchronous manner. This paper investigates the application of MMPC in active vehicle suspension design. An MMPC controller integrated with soft constraints and a Kalman filter is proposed based on a full-car model. Ride comfort, roadholding and suspension deflection are considered in this paper, where ride comfort and roadholding are formulated as a quadratic cost function in terms of sprung mass accelerations and tyre deflections, while suspension deflection performance is formulated as a hard constraint. The saturation of the actuator force is also considered and formulated as a hard constraint as well. Numerical simulation is performed with respect to different choices of weighting factors, vehicle speeds and control horizons. The results show that the overall performance of ride comfort and roadholding can be improved significantly by employing MMPC and the average time taken by MMPC to solve the individual quadratic programming problem is considerably smaller than that of the conventional MPC, which effectively demonstrate the effectiveness of the proposed method.