In order to realize fast and stable control of the linear variable parameter system, a robust model predictive control algorithm based on polyhedral invariant sets with maximum control laws is proposed. When offline, by setting a group of progressive values approaching the stable point, according to the principle that the distance from the state variable to the stable point is roughly the same, a sequence of state variable sets is constructed, and the larger control law in each set is obtained through optimization. The laws are then optimized in a backstepping way to obtain a series of maximum control laws,and are combined with the input and output constraints of the system to obtain the offline polyhedral invariant sets. When online, the actual control law of the system is obtained by linear interpolation optimization according to the position of state variables of each sampling period in the polyhedron invariant sets. The detailed steps of the offline and online algorithms and the closed-loop stability proof of the system are given. The simulation results prove the effectiveness of the proposed algorithm, and indicate that the proposed algorithm makes the closed-loop response of the system more rapid and stable.