In this paper, a new model predictive control (MPC) algorithm is developed for the polytopic linear parameter-varying (LPV) systems subject to actuator saturation. First, the set invariance of the discrete-time LPV systems subject to actuator saturation is analyzed and the invariant set is determined by solving an LMI optimization problem. The input saturation constraint is directly incorporated into the optimization problem. Then a min-max MPC algorithm is proposed based on the set invariance for the LPV systems subject to actuator saturation. A gain-scheduling MPC algorithm is also proposed for the design of the parameter-dependent controller. At last, a numerical example is present to show the effectiveness of the algorithms and their superior performance.