In　this　paper,　a　modified　Leslie-type　predator-prey　model　with　simplified　Holling　type　IV　functional　response　is　established,　in　which　double　Allee　effect　on　prey　and　nonlinear　prey　harvesting　are　considered.　The　analysis　of　the　model　shows　that　there　exists　a　Bogdanov-Takens　singularity　(focus　case)　of　codimension　4,　and　also　multiple　other　nonhyperbolic　and　degenerate　equilibria.　Bifurcations　are　explored　and　it　is　found　that　transcritical　bifurcation,　saddle-node　bifurcation,　Bogdanov-Takens　bifurcation　of　codimension　2,　degenerate　cusp　type　Bogdanov-Takens　bifurcation　of　codimension　3,　and　degenerate　focus　type　Bogdanov-Takens　bifurcation　of　codimension　4　occur　as　parameters　vary.　The　bifurcations　result　in　complex　dynamic　behaviors,　such　as　double　limit　cycle,　triple　limit　cycle,　quadruple　limit　cycle,　cuspidal　loop,　(multiple)　homoclinic　loop,　saddle-node　loop,　and　limit　cycle(s)　simultaneously　with　homoclinic　loop.　We　run　numerical　simulations　to　verify　the　theoretical　results,　and　it　is　found　that　the　system　admits　bistability,　tristability,　or　even　tetrastability.(c)　2022　International　Association　for　Mathematics　and　Computers　in　Simulation　(IMACS).　Published　by　Elsevier　B.V.　All　rights　reserved.