This　paper　investigates　the　effect　of　fear　effect　and　constant-type　harvesting　on　the　dynamic　of　a　Leslie-Gower　predator-prey　model.　Initially,　an　analysis　is　carried　out　to　identify　all　potential　equilibria　and　evaluate　their　stability.　Furthermore,　the　dynamic　behavior　at　these　points　is　examined,　revealing　various　bifurcations　such　as　saddle-node　bifurcation,　Hopf　bifurcation,　and　Bogdanov-Takens　bifurcation.　In　particular,　the　model　undergoes　a　degenerate　Hopf　bifurcation,　which　leads　to　the　existence　of　two　limit　cycles.　Additionally,　we　demonstrate　that　the　Bogdanov-Takens　bifurcation　of　codimension　2　occurs　in　this　model.　Ultimately,　these　findings　are　validated　through　numerical　simulations,　demonstrating　that　continuous　harvesting　or　the　significant　fear　effect　is　not　conducive　to　either　predator　or　prey　surviving.