The levitation control in a linear magnetic-levitation (Maglev) rail system is a subject of considerable scientific interest because of highly nonlinear and unstable behaviors. This study mainly designs a robust fuzzy-neural-network control (RFNNC) scheme for the levitated positioning of the linear Maglev rail system with nonnegative inputs. In the model-free RFNNC system, an online learning ability is designed to cope with the problem of chattering phenomena caused by the sign action in backstepping control (BSC) design and to ensure the stability of the controlled system without the requirement of auxiliary compensated controllers despite the existence of uncertainties. Moreover, the nonnegative outputs of the RFNNC system can be directly supplied to electromagnets in the Maglev system without complicated control transformations for relaxing strict constrains in conventional model-based control methodologies. The effectiveness of the proposed control schemes for the levitation control of a Maglev system is verified by numerical simulations and experimental results, and the superiority of the RFNNC system is indicated in comparison with the BSC system.