In　this　paper,　we　investigate　a　simplified　Holling　IV　type　predator-prey　model　with　weak　Allee　effect　on　prey　and　anti-predator　behavior.　First,　the　existence　and　stability　of　all　possible　equilibria　are　analyzed,　which　suggests　the　changing　trend　of　the　predator-prey　system　under　different　initial　values.　Second,　bifurcation　analysis　at　the　equilibria　are　performed　to　explore　the　dynamic　behavior　of　the　system　while　the　parameters　pass　the　critical　values,　which　reveals　the　influence　of　the　death　rate,　anti-predator　behavior　and　weak　Allee　effect　on　the　system.　It　is　found　that　the　system　undergoes　saddle-node　bifurcation,　cusp　type　Bogdanov-Takens　bifurcation　of　codimension　2　and　3,　and　Hopf　bifurcation,　forming　the　organizing　center　of　a　series　of　codimensional　bifurcations.　The　bifurcations　indicate　the　change　of　the　final　state　and　the　occurrence　of　oscillations　of　the　predator-prey　system　under　different　parameters.　Finally,　the　theoretical　results　are　confirmed　by　numerical　simulations.