The electromagnetic levitation system (ELS) of Maglev train is a strongly nonlinear, open-loop unstable system, which controls the air gap by controlling the magnitude of electromagnetic suction force through the current. ELS are suffering from many factors, such as input unidirectional constraints, maximum limited current, and external perturbations, during work. These factors pose significant challenges to the airgap stability control of the ELS system. In this paper, a continuous adaptive robust control method is proposed to address these problems simultaneously. The unidirectional constraint on the control current is handled by a series of transformation operations on the nonlinear dynamical equations, and the perturbation set sum term and unmatched term are introduced. The control law is divided into two parts, one is an update law for online estimation of unknown parameters, and the other is used to compensate for parameter uncertainties and resist external disturbances. The asymptotic stability of the closed-loop system at the equilibrium point is proved based on Lyapunov theory without linearized approximation of the original nonlinear model. Three sets of experiments are also carried out on an experimental platform, and the results demonstrate that the proposed method can track the air gap quickly and accurately, and is robust to parameter uncertainties and external disturbances.