In　Wang　and　Zhao　(2018),　the　authors　investigated　the　Rayleigh–Taylor　(abbr.　RT)　instability　in　the　compressible　viscoelastic　fluid　driven　by　the　gravity　in　a　bounded　domain　Ω　based　on　Oldroyd-B　model.　In　particular,　the　authors　proved　that　the　steady-state　is　nonlinearly　unstable　in　the　sense　of　H3(Ω)-norm　to　the　viscoelastic　RT　(abbr.　VRT)　problem.　In　this　paper,　by　switching　our　analysis　to　Lagrangian　coordinates,　we　can　show　the　nonlinear　instability　result　in　the　sense　of　L1(Ω)-norm　based　on　a　bootstrap　instability　method.　By　an　inverse　transformation　of　Lagrangian　coordinates,　we　can　further　get　the　nonlinear　instability　result　for　the　VRT　problem　in　the　sense　of　L1(Ω)-norm　in　Eulerian　coordinates,　and　thus　improve　the　instability　result　in　Wang　and　Zhao　(2018).　©　2020　Elsevier　B.V.