Because of the controllable damping characteristics, magnetorheological damper can be used to produce high-quality shock absorber.In recent years, it has been developed in the field of industrial vibration control by combining design with variety of control strategies.Researches show that the fractional model has high accuracy of fitting to the MR damper.In this paper, the viscoelastic properties of the MR damper are described by the fractional model, and the approximate fractional transfer function is obtained by the Oustaloup approximation method.A new model predictive controller is designed based on the quadratic performance index of the output tracking input after the discretization.Finally, the simulation results show that the predictive controller has good dynamic performance and verify the feasibility and stability of the design.