Graphene　reinforcements　can　obviously　enhance　the　piezoelectric　properties　as　well　as　the　mechanical　properties　of　the　polyvinylidene　fluoride　(PVDF).　This　paper　investigates　the　linear　and　nonlinear　vibration　behaviors　of　the　smart　piezoelectric　composite　plate　reinforced　by　uniformly　and　non-uniformly　dispersing　graphene　platelets　(GPLs).　The　effective　Young＇s　modulus　is　predicted　by　the　Halpin　Tsai＇s　parallel　model　while　the　effective　mass　density,　Possion＇s　ratio　and　piezoelectric　properties　are　calculated　by　the　rule　of　the　mixture.　Based　on　the　first-order　shear　deformation　plate　theory,　von　Karman　nonlinear　geometric　relationship　and　Hamilton＇s　principle,　the　governing　equations　of　motion　under　different　boundary　conditions　are　derived　for　the　smart　piezoelectric　composite　plate.　The　governing　equations　of　motion　are　solved　to　obtain　the　nonlinear　eigenvalue　equations　by　the　differential　quadrature　(DQ)　method.　The　analysis　is　validated　by　comparing　with　the　current　results　of　the　smart　piezoelectric　composite　plate.　The　effects　of　the　GPL　distribution　pattern,　stratification　number,　concentration　and　geometry　of　GPLs,　plate　geometry,　external　voltage　and　piezoelectric　properties　of　GPLs　as　well　as　boundary　conditions　on　the　linear　and　nonlinear　vibration　behaviors　are　discussed　in　detail.　The　numerical　results　clearly　illustrate　that　there　exists　the　great　potential　for　using　GPLs　in　achieving　smart　structures　with　significantly　improved　structural　stiffness.