Abstract: A robust model predictive control(MPC) algorithm based on reachable sets is designed.Firstly,a robust invariant set is established and serves as the terminal constraint set for MPC;next,the inclusion degrees of reachable sets in terminal constraint set are used as optimization index;finally,the control strategy with gradually shortened predictive horizon is adopted to guarantee the existence of the feasible solution of online optimization.It is proved in theory that any point in the region of attraction will be led to the terminal constraint set in finite horizon and then stays in this set all the time.The simulation example verifies the feasibility of the robust MPC algorithm designed.