The　nonlinear　dynamic　behaviour　of　a　new　three-phase　composite　plate　is　analysed　in　this　article.　The　plate　is　formed　at　the　top　and　bottom　surfaces　of　a　1-3　piezoelectric　fiber　composite　plate　coated　with　graphene　sheets　(MFC-GRAP).　Firstly,　the　physical　properties　of　MFC-GRAP　plate　are　calculated　through　mixture　rules.　Then,　according　to　Reddy　first-order　shear　deformation　theory,　von　Karman　displacement-strain　relationship　and　Hamilton＇s　principle,　the　nonlinear　dynamic　equations　of　MFC-GRAP　plate　are　obtained.　The　partial　differential　equations　are　discretized　into　two　degree-of-freedom　ordinary　differential　equations　by　Galerkin　method.　Finally,　the　equations　of　the　amplitude-frequency　responses　are　obtained　by　multi-scale　method.　The　effects　of　graphene　volume　fraction　on　the　amplitude-frequency　response　curves　are　discussed.　Meanwhile,　the　MATLAB　software　is　adopted　to　numerical　simulation.　The　results　show　that　the　volume　fraction　of　GRAP,　initial　values　and　damping　coefficients　have　great　effects　on　the　nonlinear　dynamic　behaviour　of　the　structure.