We　propose　a　Leslie-Gower　predator-prey　model　incorporating　a　prey　refuge.　By　constructing　a　suitable　Lyapunov　function,　we　show　that　the　unique　positive　equilibrium　of　the　system　is　globally　stable,　which　means　that　for　this　ecosystem,　prey　refuge　has　no　influence　on　the　persistent　property　of　the　system.　Mathematic　analysis　shows　that　increasing　the　amount　of　refuge　can　increase　prey　densities.　As　far　as　the　predator　species　is　concerned,　when　the　assumption　a(1)r(2)　＜=　a(2)b(1),　holds,　increasing　the　amount　of　prey　refuge　can　decrease　the　predator　densities;　when　the　assumption　a(1)r(2)　＞　a(2)b(1)　holds,　there　exists　a　threshold　m*,　such　that　for　the　prey　refuge　smaller　than　this　threshold,　increasing　the　amount　of　prey　refuge　can　increase　the　predator　densities　and　if　the　prey　refuge　is　larger　than　the　threshold,　increasing　the　amount　of　prey　refuge　can　decrease　the　predator　densities.　(C)　2009　Published　by　Elsevier　Ltd