This　paper　is　concerned　with　dynamic　stability　of　graded　graphene　reinforced　truncated　conical　shells　under　both　periodic　spinning　speeds　and　axial　loads　considering　thermal　effects.　The　volume　fraction　of　graphene　platelets　(GPLs)　varies　continuously　along　the　shell＇s　thickness　direction,　which　induces　the　position-dependent　effective　material　properties.　Based　upon　Love＇s　thin　shell　theory　and　Galerkin　approach,　the　equations　of　motion　of　the　conical　shells　are　derived　by　considering　thermal　environment,　both　time-variable　spinning　speeds　and　axial　loads.　The　method　of　multiple　scales　is　adopted　to　obtain　an　analytical　solution　on　the　instability　boundaries　under　combination　parametric　resonances.　Then,　comprehensive　parametric　studies　are　conducted　focusing　on　the　instability　regions,　natural　frequencies　and　critical　spinning　speeds　of　the　conical　shell.　The　sensitivities　of　dynamic　stabilities　on　the　thermal　expansion　deformation,　thermal　conductivity　and　temperature-dependent　material　properties　are　also　analyzed.　Results　show　that　the　conical　shell　system　would　be　always　instability　if　parametric　phase　is　not　equal　to　integer　multiple　of　pi.　The　GPL　parameters,　temperature　variation,　spinning　speeds　and　axial　loads　have　a　significant　influence　on　dynamic　stability　of　the　conical　shell,　and　thermal　conductivity　and　thermal　expansion　deformation　are　nonnegligible　in　the　dynamic　stability　analysis.