A　predator-prey　model　with　simplified　Holling　type　III　response　function　incorporating　a　prey　refuge　under　sparse　effect　is　considered.　Through　qualitative　analysis　of　the　model,　at　least　two　limit　cycles　exist　around　the　positive　equilibrium　point　with　the　result　of　focus　value,　the　Hopf　bifurcation　under　a　prey　refuge　is　obtained.　We　also　show　the　influence　of　prey　refuge.　Numerical　simulations　are　carried　out　to　illustrate　the　feasibility　of　the　obtained　results　and　the　dependence　of　the　dynamic　behavior　on　the　prey　refuge.　Through　the　results　of　computer　simulation,　it　is　further　shown　that　under　certain　conditions　the　model　has　three　limit　cycles　surrounding　the　positive　equilibrium　point.