This　paper　focuses　on　the　Rayleigh–Bénard　(abbr.　RB)　problem　of　three-dimensional　incompressible　non-Newtonian　fluids　with　Eills-type,　where　p　≥　3.　We　derive　a　threshold　Rc,　such　that　if　the　Rayleigh　numeral　R　in　the　RB　problem　of　non-Newtonian　fluids　is　bigger　than　Rc,　then　the　unique　solution　of　the　RB　problem　is　exponentially　stable　in　time.　Such　stability　result　is　proved　by　making　use　of　the　energy　method　and　the　stability　criterion.　In　addition,　we　also　provide　a　nonlinear　instability　result　for　R　∈　[0,　Rc)　by　the　bootstrap　instability　method　in　[13].　©　2024　American　Institute　of　Mathematical　Sciences.　All　rights　reserved.