A　Leslie-Gower　predator-prey　model　incorporating　harvesting　is　studied.　By　constructing　a　suitable　Lyapunov　function,　we　show　that　the　unique　positive　equilibrium　of　the　system　is　globally　stable,　which　means　that　suitable　harvesting　has　no　influence　on　the　persistent　property　of　the　harvesting　system.　After　that,　detailed　analysis　about　the　influence　of　harvesting　is　carried　out,　and　an　interesting　finding　is　that　under　some　suitable　restriction,　harvesting　has　no　influence　on　the　final　density　of　the　prey　species,　while　the　density　of　predator　species　is　strictly　decreasing　function　of　the　harvesting　efforts.　For　the　practical　significance,　the　economic　profit　is　considered,　sufficient　conditions　for　the　presence　of　bionomic　equilibrium　are　given,　and　the　optimal　harvesting　policy　is　obtained　by　using　the　Pontryagin＇s　maximal　principle.　At　last,　an　example　is　given　to　show　that　the　optimal　harvesting　policy　is　realizable.　Copyright　©　2011　Na　Zhang　et　al.