Investigated　herein　are　the　nonlinear　vibration　characteristics　of　a　rectangular　microsheet　comprising　micro　fiber　composite　with　graphene　(GP)　skin　under　coupled　excitations.　Owing　to　the　good　thermal　conductivity　of　GP,　the　heat　sink　performance　of　the　GP　skin　is　also　considered.　In　this　study,　the　constitutive　relation　for　the　microsheet　is　established　by　applying　the　Eringen　theory　and　the　governing　equations　for　nonlinear　dynamics　of　the　microsheet　are　obtained　from　the　principle　of　conservation　of　energy.　The　Green　and　Naghdi＇s　generalized　thermo-elasticity　theory　and　the　Galerkin　weighted　residual　method　are　employed　to　describe　the　thermo-elasticity　coupling　effect　of　the　MFC-GP　microsheet.　The　positive　piezoelectric　effects　of　graphene　and　MFC　are　also　taken　into　consideration.　Next,　the　coupled　ordinary　differential　equations　of　thermo-elasticity-electricity　are　obtained　by　the　Galerkin　discrete　method.　Finally,　the　nonlinear　frequency　response　equations　of　the　microsheet　are　derived　through　the　multi-scale　method.　By　using　the　global　residual　harmonic　balance　method,　nonlinear　vibration　characteristic　of　the　MFC-GP　microsheet　are　discussed　with　respect　to　nonlocal　parameters,　volume　fraction　of　graphene,　and　aspect　ratio,　which　have　a　significant　impact　on　the　dynamic　behaviors　of　the　microsheet.　The　findings　will　provide　a　theoretical　guidance　for　engineering　design　of　such　microsheets.