A　predator-prey　model　with　modified　Leslie-Gower　and　Beddington-DeAngelis　functional　response　is　studied.　The　local　stability　of　the　equilibria　and　the　permanence　of　the　system　are　investigated.　By　applying　the　fluctuation　lemma,　qualitative　analysis　and　Lyapunov　direct　method,　respectively,　three　sufficient　conditions　on　the　global　asymptotic　stability　of　a　positive　equilibrium　are　obtained.©　2014　Liu　and　Jiang;　licensee　Springer.