In　this　paper,　a　Gause　type　predator-prey　system　with　constant-yield　prey　harvesting　and　monotone　ascending　functional　response　is　proposed　and　investigated.　We　focus　on　the　influence　of　the　harvesting　rate　on　the　predator-prey　system.　First,　equilibria　corresponding　to　different　situations　are　investigated,　as　well　as　the　stability　analysis.　Then　bifurcations　are　explored　at　nonhyperbolic　equilibria,　and　we　give　the　conditions　for　the　occurrence　of　two　saddle-node　bifurcations　by　analyzing　the　emergence,　coincidence　and　annihilation　of　equilibria.　We　calculate　the　Lyapunov　number　and　focal　values　to　determine　the　stability　and　the　quantity　of　limit　cycles　generated　by　supercritical,　subcritical　and　degenerate　Hopf　bifurcations.　Furthermore,　the　system　is　unfolded　to　explore　the　repelling　and　attracting　Bogdanov-Takens　bifurcations　by　perturbing　two　bifurcation　parameters　near　the　cusp.　It　is　shown　that　there　exists　one　limit　cycle,　or　one　homoclinic　loop,　or　two　limit　cycles　for　different　parameter　values.　Therefore,　the　system　is　susceptible　to　both　the　constant-yield　prey　harvesting　and　initial　values　of　the　species.　Finally,　we　run　numerical　simulations　to　verify　the　theoretical　analysis.　(C)　2021　International　Association　for　Mathematics　and　Computers　in　Simulation　(IMACS).　Published　by　Elsevier　B.V.　All　rights　reserved.