In　this　paper,　we　investigate　the　dynamic　behavior　of　a　modified　Leslie-Gower　predator-prey　model　with　the　Allee　effect　on　both　prey　and　predator.　It　is　shown　that　the　model　has　at　most　two　positive　equilibria,　where　one　is　always　a　hyperbolic　saddle　and　the　other　is　a　weak　focus　with　multiplicity　of　at　least　three　by　concrete　example.　In　addition,　we　analyze　the　bifurcations　of　the　system,　including　saddle-node　bifurcation,　Hopf　bifurcation　and　Bogdanov-Takens　bifurcation.　The　results　show　that　the　model　has　a　cusp　of　codimension　three　and　undergoes　a　Bogdanov-Takens　bifurcation　of　codimension　two.　The　system　undergoes　a　degenerate　Hopf　bifurcation　and　has　two　limit　cycles　(the　inner　one　is　stable　and　the　outer　one　is　unstable).　These　enrich　the　dynamics　of　the　modified　Leslie-Gower　predator-prey　model　with　the　double　Allee　effects.