In　this　paper,　we　analyze　the　bifurcation　of　a　Holling-Tanner　predator-prey　model　with　strong　Allee　effect.　We　confirm　that　the　degenerate　equilibrium　of　system　can　be　a　cusp　of　codimension　2　or　3.　As　the　values　of　parameters　vary,　we　show　that　some　bifurcations　will　appear　in　system.　By　calculating　the　Lyapunov　number,　the　system　undergoes　a　subcritical　Hopf　bifurcation,　supercritical　Hopf　bifurcation　or　degenerate　Hopf　bifurcation.　We　show　that　there　exists　bistable　phenomena　and　two　limit　cycles.　By　verifying　the　transversality　condition,　we　also　prove　that　the　system　undergoes　a　Bogdanov-Takens　bifurcation　of　codimension　2　or　3.　The　main　conclusions　of　this　paper　complement　and　improve　the　previous　paper　[30].　Moreover,　numerical　simulations　are　given　to　verify　the　theoretical　results.　©　2023　the　Author(s),　licensee　AIMS　Press.　This　is　an　open　access　article　distributed　under　the　terms　of　the　Creative　Commons　Attribution　License　(http://creativecommons.org/licenses/by/4.0)