We　investigate　the　stability　of　Rayleigh–Taylor　(RT)　problem　of　the　stratified　incompressible　viscoelastic　fluids　under　the　rotation　and　the　gravity　in　a　horizontal　periodic　domain,　in　which　the　rotation　axis　is　parallel　to　the　direction　of　gravity,　the　two　fluids　are　immiscible,　and　the　heavier　fluid　lies　on　the　lighter　one.　We　establish　a　stability　condition　for　the　RT　problem.　Moreover,　we　prove　that,　under　the　stability　condition,　the　RT　problem　enjoys　a　unique　strong　solution,　which　exponentially　decays　with　respect　to　time.　In　addition,　we　note　that　the　stability　condition　is　independent　of　rotation　angular　velocity,　and　the　rotation　has　no　destabilizing　effect.　©　2018,　The　Author(s).