We　investigate　the　nonlinear　instability　of　a　viscoelastic　Rayleigh–Taylor　equilibrium　state　of　a　nonhomogeneous　incompressible　viscoelastic　fluid　in　the　presence　of　a　uniform　gravitational　field.　It＇s　well-known　that　the　viscoelastic　Rayleigh–Taylor　equilibrium　state　is　unstable　in　H2(Ω)-norm,　if　the　elasticity　coefficient　κ　is　less　than　a　critical　number　κc,　where　Ω　denotes　the　domain　occupied　by　the　viscoelastic　fluid.　In　this　article,　by　choosing　a　new　energy　functional　in　Gronwall-type　inequality,　we　show　that,　for　the　horizontal　periodic　domain　with　infinite　height,　the　viscoelastic　Rayleigh–Taylor　equilibrium　state　is　unstable　in　L2(Ω)-norm　based　on　a　bootstrap　instability　method.　©　2017　Elsevier　Inc.