Abstract: Based on the multi-parametric programming method for linear constrained optimal control problem,the explicit model predictive control systems for linear time-invariant and time-variant constrained systems are established respectively. With the proposed explicit model predictive control system,simulation are made for active vibration control of elevator mechanical system under different working conditions(light load,heavy load),and the results show that the explicit model predictive control is effective for the active vibration control of elevator mechanical system.