A　stage-structured　predator-prey　model　(stage　structure　for　both　predator　and　prey)　with　modified　Leslie-Gower　and　Holling-II　schemes　is　studied　in　this　paper.　Using　the　iterative　technique　method　and　the　fluctuation　lemma,　sufficient　conditions　which　guarantee　the　global　stability　of　the　positive　equilibrium　and　boundary　equilibrium　are　obtained.　Our　results　indicate　that　for　a　stage-structured　predator-prey　community,　both　the　stage　structure　and　the　death　rate　of　the　mature　species　are　the　important　factors　that　lead　to　the　permanence　or　extinction　of　the　system.