A　Leslie–Gower　predator–prey　model　with　Allee　effect　on　prey　and　hunting　cooperation　on　predator　is　considered.　We　show　the　solution　of　model　is　positive　and　ultimately　upper　bounded,　and　prove　the　origin　is　an　attractor　by　applying　the　blow-up　method.　The　model　has　at　most　two　positive　equilibria,　one　is　always　a　hyperbolic　saddle　and　the　other　is　a　weak　focus　of　multiplicity　at　least　two.　Moreover,　we　confirm　that　the　degenerate　equilibrium　can　be　a　cusp　of　codimension　at　most　3.　A　series　of　bifurcations　can　occur,　such　as　saddle-node　bifurcation,　Hopf　bifurcation　and　Bogdanov–Takens　bifurcation.　Selecting　Allee　effect　and　hunting　cooperation　as　bifurcation　parameters,　we　investigate　the　influence　of　Allee　effect　and　hunting　cooperation　on　the　dynamics　of　the　model.　Finally,　through　numerical　simulations,　we　illustrate　the　Allee　effects　(or　hunting　cooperation)　is　detrimental　to　the　coexistence　of　two　species　when　the　strength　of　the　Allee　parameter　(or　hunting　cooperation)　increases.　©　2024,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Switzerland　AG.