This　paper　investigates　the　linear　and　nonlinear　vibration　responses　for　the　functionally　graded　graphene-reinforced　laminated　composite　cantilever　(FG-GRLCC)　rectangular　variable　cross-section　plate　subjected　to　the　transverse　and　parametric　excitations　under　the　thermal　environment.　Halpin-Tsai　model　is　used　to　calculate　the　material　properties　of　the　graphene-reinforced　structure.　Using　the　classical　laminated　plate　theory,　von　Karman　large　deformation　theory,　Hamilton　principle　and　Galerkin　method,　the　dynamic　model　is　given　for　the　FG-GRLCC　rectangular　variable　cross-section　plate.　The　natural　frequencies　and　mode　shapes　are　analyzed　for　the　FG-GRLCC　rectangular　variable　cross-section　plate　under　the　thermal　environment　through　using　Rayleigh-Ritz　method.　The　averaged　equations　of　the　system　are　obtained　based　on　the　multiple　scale　perturbation　(MSP)　under　the　primary,　1/2　sub-harmonic　and　1:1　internal　resonances.　The　comparisons　between　the　theoretical　algorithm　and　finite　element　method　are　proposed　to　illustrate　the　accuracy　of　the　present　model.　The　results　about　the　frequency　veering　phenomenon　and　mode　shape　interaction　have　been　illustrated.　The　amplitude-frequency　response　curves　and　force-amplitude　response　curves　are　depicted　for　the　FG-GRLCC　rectangular　variable　cross-section　plate.　The　nonlinear　and　chaotic　vibrations　for　the　FG-GRLCC　rectangular　variable　cross-section　plate　is　studied　by　using　the　bifurcation　diagrams　and　max　Lyapunov　exponents.　©　2023　Elsevier　Ltd