This paper proposes an adaptive robust nonlinear controller for position tracking problem of a magnetic levitation system, which is governed by an SISO second-order nonlinear differential equation. The controller is designed in a backstepping manner based on the nonlinear system model in the presence of parameter uncertainties. At the first step, a PI controller is designed to stabilize the position error of the levitated object. Then at the second step, an adaptive robust nonlinear controller composed of an adaptive feedback linearization control term and a robust nonlinear damping term is designed, to attenuate the effects of parameter uncertainties. The combined adaptive and robust approach helps to overcome some well-known practical problems such as high-gain feedback of the robust controller, and poor transient performance of the adaptive controller, so that better control performance can be achieved compared to the case where either is employed alone. Experimental results are included to show the excellent position tracking performance of the designed control system.