Model-based predictive control (MBPC) is an emerging design tool in process control, thanks to its capability to incorporate several attributes fundamental in practical applications. On the other hand, multirate control systems are able to describe various practical situations where technological constraints require that sensor measurements and control calculations are performed at different times and rates. For these reasons, it seems appropriate to extend MBPC to the multirate case. Then, a design procedure is developed in this paper, leading to a multirate controller which guarantees stability and zero error asymptotic regulation to the overall control system.