The　dynamic　stability　of　an　axially　moving　graphene　reinforced　laminated　composite　plate　is　studied.　The　graphene　nanoplatelets　(GPLs)　are　distributed　in　each　polyvinylidene　fluoride　(PVDF)　layer　uniformly　and　in　the　whole　plate　symmetrically.　The　volume　fraction　of　the　first　layer　is　used　as　the　control　variable　to　determine　the　distribution　pattern　of　the　GPLs.　Halpin-Tsai＇s　model　is　used　to　predict　the　effective　Young＇s　modulus　of　the　axially　moving　graphene　reinforced　laminated　composite　plate.　The　effective　mass　density　and　Poisson＇s　ratio　are　calculated　by　using　the　rule　of　mixture.　Based　on　von　Karman　plate　theory　and　Hamilton＇s　principle,　the　governing　equations　of　motion　are　derived　for　the　axially　moving　graphene　reinforced　laminated　composite　plate.　To　evaluate　the　stability　of　the　axially　moving　graphene　reinforced　laminated　composite　plate　with　the　constant　velocity,　the　ordinary　differential　equations　of　motion　are　obtained　by　using　Galerkin　method.　The　effect　of　the　graphene　reinforcement　on　the　critical　and　flutter　velocities　of　the　axially　moving　laminated　composite　plate　is　analyzed　based　on　the　eigenvalue　of　the　coefficient　matrix.　The　influence　of　the　graphene　reinforcement　on　the　instability　region　for　the　axially　moving　laminated　composite　plate　with　the　varied　velocity　is　also　evaluated　by　using　the　direct　multiscale　method.