Graphene is a new type of carbon nano-material, which can be utilized to enhance composites for excellent mechanical properties. In this paper, the nonlinear dynamic behavior of a grapheme-reinforced composite plate under cantilever boundary condition was studied. The equivalent Young's modulus of the composite plate was calculated by Halpin-Tsai model. The nonlinear dynamic equations of the composite plate were obtained by using the first-order laminated plate theory and Hamilton’s principle. The governing equations of transverse displacements of the composite plate were obtained by modal condensation. The Rayleigh-Ritz method was used to calculate the natural frequencies of the composite plate. It was found that there exists are lationship of 1:3 between the second and fourth order natural frequencies of the composite plate. The nonlinear vibration responses of the composite plate under 1:3 resonance was studied by using the multi-scale method. The influence of external excitation on the nonlinear vibration responses was analyzed by numerical simulation. The results showed that the transverse excitation has a great influence on the nonlinear dynamic behavior of the composite plate.