We　investigate　stability　of　an　equilibrium　state　to　a　nonhomogeneous　incompressible　viscoelastic　fluid　driven　by　gravity　in　a　bounded　domain　Omega　subset　of　R-3　of　class　C-3.　First,　we　establish　a　critical　number　kappa(C),　which　depends　on　the　equilibrium　density　and　the　gravitational　constant,　and　is　a　threshold　of　the　elasticity　coefficient　kappa　for　instability　and　stability　of　the　linearized　perturbation　problem　around　the　equilibrium　state.　Then　we　prove　that　the　equilibrium　state　is　exponential　stability　provided　that　kappa　＞　kappa(C)　and　the　initial　disturbance　quantities　around　the　equilibrium　state　satisfy　some　relations.　In　particular,　if　the　equilibrium　density　(rho)　over　bar　is　a　Rayleigh-Taylor　(RT)　type　and　(rho)　over　bar＇　is　a　constant,　our　result　strictly　shows　that　the　sufficiently　large　elasticity　coefficient　can　prevent　the　RT　instability　from　occurrence.　(C)　2016　Elsevier　Inc.　All　rights　reserved.