A　predatorprey　model　with　Holling　type　II　functional　response　incorporating　a　constant　prey　refuge　and　independent　harvesting　in　either　species　is　investigated.　Some　sufficient　conditions　of　the　instability　and　stability　properties　to　the　equilibria　and　the　existence　and　uniqueness　to　limit　cycles　for　the　model　are　obtained.　We　also　show　that　influence　of　prey　refuge　and　harvesting　efforts　on　equilibrium　density　values.　One　of　the　surprising　finding　is　that　for　fixed　prey　refuge,　harvesting　has　no　influence　on　the　final　density　of　the　prey　species,　while　the　density　of　predator　species　is　decreasing　with　the　increasing　of　harvesting　effort　on　prey　species　and　the　fixation　of　harvesting　effort　on　predator　species.　Numerical　simulations　are　carried　out　to　illustrate　the　obtained　results　and　the　dependence　of　the　dynamic　behavior　on　the　harvesting　efforts　or　prey　refuge.　©　2010　World　Scientific　Publishing　Company.