Purpose: This paper considers the air gap tracking problem of the levitation control system for medium and low-speed maglev vehicles subject to magnetic nonlinearities and track irregularities. Method: The static and dynamic magnetic field characteristics are investigated, and an improved electromagnetic force model to consider both the magnetic saturation and eddy current effect is developed. By merging neural networks (NNs), a robust adaptive control scheme is proposed, which can deal with the modeling uncertainties and magnetic nonlinearities without requiring precise model information, leading to enhanced levitation performance from the aspects of suspension safety and ride comfort. Based on the Lyapunov method, the continuity of the control signal and uniformly ultimately boundedness(UUB) of all closed-loop signals can be guaranteed. Results and conclusion: With the dynamic model of the whole suspension bogie and random irregularities, numerical simulations under various operation conditions, including constant speed, horizontal curve and vertical curve, validating the developed control scheme improves the suspension safety while maintaining the ride comfortability for passengers.