Functionally　graded　(FG)　graphene　reinforced　composite　(GRC)　is　a　new　class　of　advanced　composite　materials.　In　GRC,　several　layers　of　graphene　platelets　(GPLs)　are　randomly　or　uniformly　dispersed　in　matrix.　These　GPLs　have　uniform　arrangement,　or　are　arranged　with　gradient,　in　the　direction　of　thickness　in　accordance　with　three　different　graphene　distribution　rules.　In　this　study,　the　nonlinear　dynamic　analysis　of　FG　GRC　truncated　conical　shells,　subjected　to　a　combined　action　of　transverse　excitation　and　axial　force,　is　performed　using　the　first　shear　deformation　theory　(FSDT).　Estimation　of　equivalent　Young＇s　modulus　of　the　composites　is　calculated　using　a　modified　Halpin-Tsai　model.　In　addition,　a　partial　differential　equation　model　is　developed　based　on　the　Hamilton　principle　and　nonlinear　strain-displacement　relationship.　The　Galerkin　method　and　the　fourth-order　Runge-Kutta　method　are　used　to　solve　the　equation.　The　dimensionless　linear　natural　frequency　of　an　FG　GRC　truncated　conical　shell　is　calculated　by　the　Rayleigh-Ritz　method　and　compared　with　available　results　in　the　literature　to　verify　the　accuracy　of　the　present　model.　Simultaneously,　significant　effects　of　the　different　parameters,　such　as　the　total　layer　numbers,　semi-vertex　angles,　GPLs　weight　fractions,　distribution　patterns　and　the　length-to-thickness　ratios,　on　the　nonlinear　dynamics　including　bifurcation　and　chaos　of　FG　GRC　truncated　conical　shells　are　investigated.