In this paper,the nonlinear dynamic characteristics of simple supported plate structures of 13 type piezoelectric fiber composites (MFCGP) coated with graphene were studied. First,the nonlinear partial differential equation of the MFCGP composite material plate was deduced based on the Reddy firstorder shear deformation theory,Von Kármán displacement strain relation and Hamilton principle. Then,it was discretized into twodegreeoffreedom ordinary differential equation by the Galerkin method. Furthermore,the frequencyresponse equation with internal resonance 1:1 was obtained by the multiscale method,and the effects of volume fraction of graphene,voltage,temperature and initial phase on the frequency response curve were analyzed. Finally,the vibration response of MFCGP composite plate was investigated by using bifurcation diagram,phase diagram and waveform through numerical simulations. The results were shown complex nonlinear vibrations of the plate with different parameters and external excitations,which would have certain guiding significance for future engineering application.