This　paper　analyses　the　buckling　characters　of　a　multi-layered　functionally　graded　graphene　nanoplatelets　reinforced　nonlocal　piezoelectric　(FG-GRNP)　microplate.　The　FG-GRNP　microplate　is　acted　by　the　in-plane　axial　force　and　external　potential.　Graphene　nanoplatelets　are　assumed　to　dispersing　parallel　in　each　layer　of　the　FG-GRNP　microplate,　but　it　is　distributed　graded　along　the　thickness　direction.　The　rule　of　mixture　and　Halpin-Tsai　parallel　model　are　used　to　calculate　the　properties　of　the　FG-GRNP　microplate.　The　governing　equations　of　buckling　behaviors　the　FG-GRNP　microplate　are　derived　by　nonlocal　elastic　theory,　minimum　potential　energy　principle　and　first-order　shear　deformation　plate　theory.　The　differential　quadrature　(DQ)　method　is　adopted　to　solve　the　eigenvalue　equations.　The　effects　of　the　axial　forces,　piezoelectric　multiple,　nonlocal　parameter,　external　voltage,　characteristics　of　graphene　nanoplatelets　on　the　critical　buckling　load　of　the　FG-GRNP　microplate　are　studied.　©　2020　Institute　of　Physics　Publishing.　All　rights　reserved.