Smart　magneto-electro-elastic　(MEE)　structures　with　high　performance　are　highly　valuable　across　a　vast　range　of　aerospace　and　industrial　applications　like　smart　sensing,　space　robotics,　energy　harvesting　and　biomedical　research.　This　work　focuses　on　the　nonlinear　dynamic　response　of　a　functionally　graded　MEE　nanobeam.　Initial　geometric　imperfection　including　global　and　localized　imperfection　modes　is　considered　to　reflect　the　effect　of　undesired　error　during　nanofabrication　process.　Such　geometric　imperfection　is　involved　by　the　product　of　hyperbolic　and　trigonometric　functions.　The　nonlinear　dynamic　model　for　the　FG-MEE　nanobeam　is　established　according　to　Hamilton＇s　principle　and　nonlocal　constitutive　relation　to　derive　its　governing　equations　of　motion.　The　interaction　between　the　imperfect　FG　nanobeam　and　its　multi-physical　stimulus　is　numerically　solved　via　differential　quadrature　method.　After　validating　the　proposed　model　with　existing　works,　the　parametric　study　is　conducted　to　fully　reveal　the　coupling　effect　of　geometric　imperfection　and　numerous　parameters　including　imperfection　mode　and　amplitude,　external　electric　and　magnetic　potentials,　functionally　graded　index,　boundary　constraint　and　size-dependent　parameter　on　nonlinear　dynamic　response　of　the　FG-MEE　nanobeam.　Simulation　results　have　demonstrated　the　significance　of　the　MEE　coupling　effect,　which　can　be　used　as　a　guide　to　design　smart　and　advanced　devices　for　aerospace　and　industrial　applications.