As　a　part　of　the　rocket　structure,　the　truncated　conical　shell　will　undergo　extremely　high　temperature　changes　during　the　launch　and　flight　of　the　rocket,　which　is　particularly　important　for　the　selection　of　materials.　The　graphene-reinforced　aluminum-based　composites　(GRA)　are　widely　used　as　a　new　type　of　high-performance　material.　This　paper　mainly　studies　the　natural　vibration　characteristics　of　the　graphene-reinforced　aluminum-based　rotating　truncated　conical　(GRA-RTC)　shell　under　the　unified　boundary　conditions　by　the　traveling　wave　vibration.　The　innovation　is　to　consider　the　temperature　change　with　thickness　in　the　GRA-RTC　shell,　and　there　are　five　uniformly　distributed　artificial　springs　at　the　large　and　small　end　radii　of　the　rotating　conical　shell,　which　can　obtain　different　elastic　support　boundary　conditions.　Three　graphene　distribution　types　are　obtained　along　the　thickness　direction.　The　impact　of　the　Coriolis　force　and　initial　ring　tensor　on　the　vibration　of　the　rotating　conical　shell　is　examined　in　the　structure.　According　to　the　first-order　shear　deformation　theory　(FSDT),　strain-displacement　relationship　and　constitutive　relationship,　the　kinetic　energy　and　potential　energy　are　obtained　for　the　GRA-RTC　shell.　While　solving,　the　mode　shapes　of　the　circumferential　direction　and　generatrix　direction　of　the　rotating　conical　shell　are　given　by　using　trigonometric　functions　and　Chebyshev　polynomials.　The　ordinary　differential　equations　of　the　GRA-RTC　shell　are　attained　by　the　Rayleigh-Ritz　method,　and　the　frequency　and　mode　shapes　are　further　solved　for　the　GRA-RTC　shell.　This　paper　compares　the　results　with　Sanders＇　shell　theory　and　ANSYS　Workbench,　which　fully　verifies　the　accuracy　of　the　results　in　this　paper.　The　influences　of　the　spring　stiffness,　graphene　mass　fraction,　distribution　type,　temperature,　boundary　conditions　and　rotational　speed　on　the　frequency　and　mode　are　investigated　for　the　GRA-RTC　shell.　In　the　study　of　free　vibration　processes,　it　is　found　that　changes　in　rotational　speed　can　cause　mode　exchange,　critical　resonance　speed,　and　critical　speed　phenomena,　which　are　very　dangerous　and　can　cause　structural　failure　and　damage.　It　provides　a　foundation　for　further　research　on　nonlinear　traveling　vibration　of　the　rotating　conical　shells.　This　paper　presents　a　novel　approach　to　studying　rotating　cylindrical　and　conical　shells　with　various　boundary　conditions.