In　this　paper,　we　introduce　constant-yield　prey　harvesting　into　the　Holling-Tanner　model　with　generalist　predator.　We　prove　that　the　unique　positive　equilibrium　is　a　cusp　of　codimension　4.　As　the　parameter　values　change,　the　system　exhibits　degenerate　Bogdanov-Takens　bifurcation　of　codimension　4.　Using　the　resultant　elimination　method,　we　show　that　the　positive　equilibrium　is　a　weak　focus　of　order　2,　and　the　system　undergoes　degenerate　Hopf　bifurcation　of　codimension　2　and　has　two　limit　cycles.　By　numerical　simulations,　we　demonstrate　that　the　system　exhibits　homoclinic　bifurcation　and　saddle-node　bifurcation　of　limit　cycles　as　the　parameters　are　varied.　The　main　results　show　that　constant-yield　prey　harvesting　and　generalist　predator　can　lead　to　complex　dynamic　behavior　of　the　model.　©　2024　World　Scientific　Publishing　Company.