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.　©　2016　Elsevier　Ltd