This　paper　aims　to　study　the　dynamic　behavior　of　a　logistic　model　with　feedback　control　and　Allee　effect.　We　prove　the　origin　of　the　system　is　always　an　attractor.　Further,　if　the　feedback　control　variable　and　Allee　effect　are　big　enough,　the　species　goes　extinct.　According　to　the　analysis　of　the　Jacobian　matrix　of　the　corresponding　linearized　system,　we　obtain　the　threshold　condition　for　the　local　asymptotic　stability　of　the　positive　equilibrium　point.　Also,　we　study　the　occurrence　of　saddle-node　bifurcation,　supercritical　and　subcritical　Hopf　bifurcations　with　the　change　of　parameter.　By　calculating　a　universal　unfolding　near　the　cusp　and　choosing　two　parameters　of　the　system,　we　can　draw　a　conclusion　that　the　system　undergoes　Bogdanov-Takens　bifurcation　of　codimension-2.　Numerical　simulations　are　carried　out　to　confirm　the　feasibility　of　the　theoretical　results.　Our　research　can　be　regarded　as　a　supplement　to　the　existing　literature　on　the　dynamics　of　feedback　control　system,　since　there　are　few　results　on　the　bifurcation　in　the　system　so　far.