The　nonlinear　flutters　of　a　truncated　conical　shell,　which　is　subjected　to　aerodynamic　pressure　and　aerodynamic　heating,　are　researched.　Material　properties　with　gradient　features　along　the　radial　direction　depend　on　the　temperature.　The　supersonic　aerodynamic　force　is　obtained　by　applying　the　first-order　piston　theory,　including　the　correction　factor　for　curvature.　The　temperature　in　the　external　surface　of　the　functionally　graded　material　truncated　conical　shell　rises　as　a　result　of　viscous　aerodynamic　heating,　and　the　temperature　distribution　along　the　thickness　can　be　described　by　polynomial　series.　Hamilton＇s　principle　is　utilized　to　obtain　the　nonlinear　partial　differential　equilibrium　equation　of　the　system.　Using　Galerkin＇s　method,　a　high-dimensional　nonlinear　system　can　be　derived.　Without　considering　the　parts　of　nonlinear　terms　and　the　external　forcing　excitation,　the　flutter　boundaries　are　obtained　by　solving　the　eigenvalues　problem.　The　influences　of　ratios　of　top　radius　to　thickness,　semi-vertex　angle,　and　volume　fraction　index　on　nonlinear　dynamic　characteristics　of　functionally　graded　material　truncated　conical　shell　are　studied　in　detail　by　the　fourth-order　Runge-Kutta　algorithm.