We　study　the　predator-prey　model　proposed　by　Aziz-Alaoui　and　Okiye　(Appl.　Math.　Lett.　16　(2003)　10691075)　First,　the　structure　of　equilibria　and　their　linearized　stability　is　investigated.　Then,　we　provide　two　sufficient　conditions　on　the　global　asymptotic　stability　of　a　positive　equilibrium　by　employing　the　Fluctuation　Lemma　and　Lyapunov　direct　method,　respectively.　The　obtained　results　not　only　improve　but　also　supplement　existing　ones.　Copyright　©　2012　Shengbin　Yu.