This paper is devoted to linear astatic regulator design using model predictive control (MPC) with the application to magnetic levitation plant. The control objective is the stabilization of a metal ball position at the given point in the air by means of electromagnet. The considered mathematical model is nonlinear with input and output constraints and external disturbances. This allows to state that MPC strategy is a quite suitable approach to be used here. In this paper the algorithm for linear astatic MPC regulator design is proposed. This algorithm is based on predictive model representation in the form of augmentations. The effectiveness of the approach is demonstrated by real-time experiments for a particular magnetic levitation plant.