We　mathematically　investigate　the　Rayleigh-Taylor　(abbr.　RT)　instability　in　the　compressible　viscoelastic　fluid　in　the　presence　of　a　uniform　gravitational　field　in　a　bounded　domain　based　on　Oldroyd-B　model.　We　first　analyze　the　linearized　equations　around　the　viscoelastic　RT　equilibrium　solution,　and　obtain　an　instability　condition.　Then　we　construct　solutions　of　the　linearized　viscoelastic　RT　problem　that　grow　in　time　in　the　Sobolev　space　H-3　under　an　instability　condition,　thus　leading　to　the　linear　instability.　Finally,　with　the　help　of　the　constructed　unstable　solutions　of　the　linearized　viscoelastic　RT　problem　and　a　local　well-posedness　result　of　smooth　solutions　to　the　nonlinear　viscoelastic　RT　problem,　we　mathematically　prove　the　instability　of　viscoelastic　RT　(abbr.　VRT)　problem　in　the　sense　of　Hadamard.　(C)　2018　Elsevier　Inc.　All　rights　reserved.