A　Leslie-Gower　predator　prey　model　with　density　dependent　birth　rate　on　prey　species　and　prey　refuge　is　proposed　and　studied　in　this　paper.　Sufficient　condition　which　ensure　the　global　stable　of　the　positive　equilibrium　is　obtained.　Our　study　indicates　density　dependent　birth　rate　of　prey　species　has　negative　effect　on　the　final　density　of　both　prey　and　predator　species.　Density　dependent　birth　rate　may　lead　to　the　Allee　effect　of　prey　species　and　enhance　the　extinction　chance　of　the　species.　Numeric　simulations　are　carried　out　to　show　the　feasibility　of　the　main　results.　©　2023　The　Author(s).