Based on expressions of total kinetic energy, potential energy and electromagnetic force, the nonlinear magneto-elastic vibration equations of an axially moving current-conducting thin plate in magnetic field were deduced by using Hamilton principle. According to displacement mode hypothesis, by using the Galerkin method, a duffing magneto-elastic vibration equation of axially moving strip plate with two opposite edges simply supported in transverse magnetic field was obtained. Combination resonance amplitude-frequency equation was derived by means of the multiple-scale method, and the critical condition of stability of steady-state solution was also given. By several numerical examples, the variation curves of the amplitude for different axial speeds, magnetic induction intensities, external excitations and axial tensions were obtained respectively, then time history plot and phase plot were also obtained. The influences of different parameters on the resonance amplitudes and nonlinear characteristic behaviors were investigated, and the quasi-periodic, chaotic motion of axially moving system were further discussed.