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.　©　World　Scientific　Publishing　Company.