Titanium　alloys　are　widely　used　for　blades　due　to　their　favorable　combination　of　high　strength,　low　density　and　fatigue　resistance.　Dispersing　graphene　platelets　(GPLs)　into　titanium　alloy　in　a　layer-wise　manner　to　develop　novel　functionally　graded　(FG)　GPL/titanium　alloy　blades　can　achieve　further　enhanced　mechanical　performance.　This　paper　first　proposes　a　functionally　graded　graphene/titanium　alloy　composite　trapezoid　plate　to　investigate　the　nonlinear　free　vibration　of　rotating　blades　with　varying　cross-sections.　It　is　assumed　that　graphene　platelets　are　uniformly　dispersed　in　each　layer　of　titanium　alloy,　and　the　weight　fraction　of　GPLs　increases　from　the　middle　layer　to　the　top　layers.　The　effective　Young＇s　modulus,　effective　Poisson＇s　ratio　and　mass　density　are　calculated　by　the　modified　Halpin-Tsai　model　and　the　rule　of　mixture,　respectively.　The　discretized　motion　equations　of　the　functionally　graded　graphene　platelets　reinforced　composite　(FG-GPLRC)　trapezoid　plate　are　derived　by　the　energy　method　and　Lagrange　equations.　The　Rayleigh-Ritz　method　and　direct　iterative　process　are　applied　to　obtain　the　linear　frequencies　and　nonlinear　frequencies,　respectively.　A　detailed　numerical　study　is　carried　out　to　investigate　the　effects　of　the　material　parameters　and　dimensional　parameters　on　the　linear　and　nonlinear　free　vibrations　of　the　rotating　FG-GPLRC　trapezoid　plate.