We propose a robust model predictive control algorithm based on polyhedral invariant sets with minimum decay rates for a class of polytopic linear variable parameter systems with input and output constraints. The proposed algorithm is divided into an online part and offline part. To enhance the system control effect and improve the system response speed, the offline algorithm first seeks a minimum decay rate of the state variables to optimize a series of state variables and the corresponding state feedback control laws, and then constructs the corresponding polyhedral invariant set sequences. Based on the current measured state variables, the online algorithm determines the minimum polyhedral invariant set of the state variables in polyhedral invariant set sequences, and the control input of the system is obtained through online optimization. The detailed steps of the robust model predictive control algorithm and the closed-loop stability proof of the system are given. The simulation results verify the effectiveness of the proposed algorithm and indicate that the proposed algorithm makes the closed-loop response of the system more rapid and stable.