We　propose　a　single-species　population　model　with　partial　pollution　tolerance　in　a　polluted　environment　in　this　contribution,　and　introduce　the　random　perturbation　of　the　birth　rate　of　single-species　population　into　this　model.　The　extinction　occurs　around　the　pollution-free　equilibrium　under　some　moderate　conditions,　and　the　stationary　distribution　with　ergodicity　is　derived　around　the　positive　equilibrium.　Numerical　simulations　demonstrate　the　efficiency　of　our　main　results.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.