This　article　tries　to　investigate　the　nonlinear　free　vibration　(NFV)　response　of　magneto-electro-elastic　(MEE)　composite　plates　considering　von　Karman＇s　nonlinear　strain–displacement　theory　under　the　high　order　shear　deformation　theory　(HSDT).　The　governing　equations　are　derived　via　Hamilton＇s　principle.　The　nonlinear　motion　equations　are　dimensionless　and　solved　by　the　Galerkin　method　and　harmonic　balance　method.　Thereout,　the　nonlinear　relationship　curves　of　the　dimensionless　frequency　ratio　and　free　vibration　amplitude　of　MEE　plate　under　two　degrees　of　freedom　are　given　respectively.　According　to　the　parametric　method,　the　effects　of　the　aspect　ratio,　span-thickness　ratio,　and　magnetic　and　electric　potential　on　the　NFV　behavior　of　MEE　plates　are　analyzed.　The　differences　in　nonlinear　free　vibration　of　the　MEE　plate　under　different　degrees　of　freedom　are　discussed.　This　paper　also　verifies　the　reliability　of　the　method　and　results　by　comparing　them　with　the　published　literature.　©　2022　Elsevier　B.V.