This paper proposes a multistage suboptimal model predictive control (MPC) strategy which can reduce the prediction horizon without compromising the stability property. The proposed multistage MPC requires a precomputed sequence of *j*-step admissible sets, where the *j*-step admissible set is the set of system states that can be steered to the maximum positively invariant set in *j* control steps. Given the precomputed admissible sets, multistage MPC first determines the minimum number of steps *M* required to drive the state to the terminal set. Then, it steers the state to the (*M* – *N*)-step admissible set if *M* > *N*, or to the terminal set otherwise. The paper presents the offline computation of the admissible sets, and shows the feasibility and stability of multistage MPC for systems with and without disturbances. A numerical example illustrates that multistage MPC with *N* = 5 can be used to stabilize a system which requires MPC with *N* ≥ 14 in the absence of disturbances, and requires MPC with *N* ≥ 22 when affected by disturbances.