This paper presents a nonlinear model predictive control (MPC) method to solve the problem of regulating the suspension air gap in a magnetic levitation system in the presence of disturbances. The method iteratively linearizes the system model at each prediction step around the operating point. Then it finds linear matrix inequalities (LMI) describing upper bounds for the remaining nonlinearities and finally obtains the control signal by solving the LMIs and applying it to the original nonlinear system. A main advantage of the proposed method is that it removes the linear approximation error present in conventional linerarization-based NMPC methods.