A novel closed-loop model-based predictive control (MPC) strategy for input-saturated polytopic linear parameter varying (LPV) discrete-time systems is proposed. It is postulated that the plant belongs to a polytopic family of linear systems, each member of which being parameterized by the value that a parameter vector assumes in the unit simplex. Such a parameter can be measured online and used for feedback while a bound on its rate of change is known and exploited for predictions. The contribution of this note is to extend the MPC scheme presented in [5] for the restricting case of 1-step long control horizons to the general case of control horizons of arbitrary length N. This is done by suitably modifying the robust MPC scheme presented in [7] for uncertain polytopic systems. Feasibility and closed-loop stability of this strategy are proved and a numerical example is also presented in order to show how the freedom of extending the control horizon and the knowledge of the parameter is significant in order to improve the performance of the control strategy.