This　paper　considers　a　Leslie-Gower　predator-prey　system　with　Allee　effect　and　prey　refuge.　By　considering　the　prey　refuge　constant　as　a　parameter,　we　analyze　the　stability　of　the　equilibria　in　the　system,　and　find　that　there　are　abundant　dynamic　behaviors.　It　is　shown　that　the　model　can　undergo　a　sequence　of　bifurcations　including　saddle-node　bifurcation,　Hopf　bifurcation　and　Bogdanov-Takens　bifurcation　of　codimension　two　or　three　as　the　parameters　vary.　Moreover,　the　model　underdoes　a　degenerate　Hopf　bifurcation　of　codimension　two　and　has　two　limit　cycles,　where　the　inner　one　is　stable　and　the　outer　one　is　unstable.　Through　some　numerical　simulations,　the　occurrence　of　Bogdanov-Takens　bifurcation　and　Hopf　bifurcation　of　codimension　two　are　confirmed.