•A new damper, which can achieve different damping modes, is applied to vehicle suspension.•The hybrid dynamics of the air suspension with the new damper are modeled using MLD systems.•The optimal control of the switching sequences of the damping modes is achieved by MPC method. This paper presents the hybrid modeling and the model predictive control of an air suspension system with damping multi-mode switching damper. Unlike traditional damper with continuously adjustable damping, in this study, a new damper with four discrete damping modes is applied to vehicle semi-active air suspension. The new damper can achieve different damping modes by just controlling the on-off statuses of two solenoid valves, which makes its damping adjustment more efficient and more reliable. However, since the damping mode switching induces different modes of operation, the air suspension system with the new damper poses challenging hybrid control problem. To model both the continuous/discrete dynamics and the switching between different damping modes, the framework of mixed logical dynamical (MLD) systems is used to establish the system hybrid model. Based on the resulting hybrid dynamical model, the system control problem is recast as a model predictive control (MPC) problem, which allows us to optimize the switching sequences of the damping modes by taking into account the suspension performance requirements. Numerical simulations results demonstrate the efficacy of the proposed control method finally.