The　comparative　researches　of　the　nonlinear　vibrations　are　obtained　among　the　pure　polymer　plate　and　three　types　of　graphene　platelet　reinforced　polymer　composite　plates　under　combined　the　transverse　and　parametric　excitations.　All　edges　of　the　pure　polymer　and　graphene　platelet　reinforced　polymer　composite　plates　are　simply　supported.　Both　the　uniform　and　functionally　graded　distribution　forms　of　the　graphene　platelets　are　considered.　The　differential　governing　equations　of　motion　for　the　pure　polymer　and　graphene　platelet　reinforced　polymer　composite　plates　are　derived　based　on　the　first-order　shear　deformation　plate　theory,　von　K?rm?n　strain　displacement　relationship　and　Hamilton　principle.　The　fourth-order　Galerkin　truncation　is　employed　to　discretize　the　partial　differential　governing　equations　of　motion　to　four-degree-of-freedom　nonlinear　dynamical　system.　The　natural　frequencies　of　the　first　four　vibration　modes　are　examined　for　the　pure　polymer　and　graphene　platelet　reinforced　polymer　composite　plates　with　different　geometric　characteristics.　In　order　to　compare　the　nonlinear　vibrations　of　the　prestressed　pure　polymer　and　prestressed　graphene　platelet　reinforced　polymer　composite　plates　subjected　to　the　transverse　point　excitation　and　in-plane　uniaxial/biaxial　excitations,　the　time　histories,　phase　portraits　and　Poincare　maps　are　presented.　Some　validated　results　are　conducted　to　present　the　accuracy　of　the　present　approach.　The　effects　of　the　distribution　forms　and　weight　fractions　of　the　graphene　platelets　on　the　nonlinear　vibrations　for　the　graphene　platelet　reinforced　polymer　composite　plates　are　investigated　in　detail.　The　research　results　demonstrate　that　the　nonlinear　vibration　behaviors　of　the　prestressed　pure　polymer　plate　under　the　complex　excitations　can　be　remarkably　stabilized　by　the　reinforcement　of　the　graphene　platelets.