In　this　paper,　we　investigate　the　stability　and　bifurcation　of　a　Leslie-Gower　predator-prey　model　with　a　fear　effect　and　nonlinear　harvesting.　We　discuss　the　existence　and　stability　of　equilibria,　and　show　that　the　unique　equilibrium　is　a　cusp　of　codimension　three.　Moreover,　we　show　that　saddle-node　bifurcation　and　Bogdanov-Takens　bifurcation　can　occur.　Also,　the　system　undergoes　a　degenerate　Hopf　bifurcation　and　has　two　limit　cycles　(i.e.,　the　inner　one　is　stable　and　the　outer　is　unstable),　which　implies　the　bistable　phenomenon.　We　conclude　that　the　large　amount　of　fear　and　prey　harvesting　are　detrimental　to　the　survival　of　the　prey　and　predator.　©　2023　American　Institute　of　Mathematical　Sciences.　All　rights　reserved.