We　consider　a　predator-prey　model　with　Holling　type　II　functional　response　incorporating　a　constant　prey　refuge　and　a　constant-rate　prey　harvesting.　Depending　on　the　constant　prey　refuge　m,　which　provides　a　condition　for　protecting　m　of　prey　from　predation,　and　the　constant-rate　prey　harvesting,　some　sufficient　conditions　for　the　instability　and　global　stability　of　the　equilibria,　and　the　existence　and　uniqueness　of　limit　cycles　of　the　model　are　obtained.　We　also　show　the　influences　of　prey　refuge　and　harvesting　efforts　on　equilibrium　density　values.　Numerical　simulations　are　carried　out　to　illustrate　the　feasibility　of　the　obtained　results　and　the　dependence　of　the　dynamic　behavior　on　the　harvesting　efforts　or　prey　refuge.　(C)　2009　Elsevier　Ltd.　All　rights　reserved.