The　eccentric　rotating　cylindrical　shell　structure　has　an　important　application　prospect　in　aerospace　engineering　field,　such　as　space　annular　antenna.　In　this　paper,　the　dynamic　model　of　an　eccentric　rotating　functionally　graded　grapheme　platelets　reinforced　composite　(FG-GPLRC)　cylindrical　shell　based　on　the　first-order　shear　deformation　theory　is　established.　The　free　vibration　and　buckling　analyses　of　the　eccentric　rotating　FGGPLRC　cylindrical　shell　under　the　axial　excitation　are　presented.　Taking　into　account　the　influences　of　the　Coriolis　force　and　centrifugal　force　caused　by　eccentric　rotation.　Considering　five　grapheme　platelets　(GPLs)　distribution　patterns　of　the　FG-GPLRC　cylindrical　shell,　and　the　modified　Halpin-Tsai　model　is　used　to　calculate　the　effective　Young＇s　modulus.　By　utilizing　the　Hamilton　principle,　the　first-order　shear　deformation　shell　theory　and　the　von-Karman　type　nonlinear　geometric　relationships,　a　system　of　the　partial　differential　governing　equations　for　the　eccentric　rotating　FG-GPLRC　cylindrical　shell　is　derived.　Then,　the　ordinary　differential　equations　of　the　cylindrical　shell　are　obtained　according　to　Galerkin　method.　The　influences　of　the　GPLs　distribution　pattern,　weight　fraction,　eccentric　distance,　ratio　of　radius　to　thickness,　ratio　of　length　to　radius,　as　well　as　rotating　speed　of　the　eccentric　rotating　FG-GPLRC　cylindrical　shell　on　the　buckling　and　free　vibration　behaviors　are　discussed.