We　consider　the　dynamical　behaviors　of　the　single　species　logistic　model　considering　Allee　effect　together　with　feedback　control　in　this　paper.　By　using　the　method　of　formal　power　series　of　Poincaré,　we　put　forward　sufficient　conditions　for　the　positive　equilibrium　to　be　a　stable　(unstable)　finefocus　with　order　at　1　or　a　unstable　fine-focus　with　order　at　2.　Qualitative　analysis　of　the　model　indicates　the　ultimate　boundedness　of　the　positive　solutions　to　the　system,　and　when　the　positive　equilibrium　is　unstable,　we　obtain　sufficient　conditions　that　sustain　a　unique　stable　limit　cycle.　Finally,　numerical　simulations　are　conducted　to　validate　the　major　conclusions.　©　2022.　IAENG　International　Journal　of　Applied　Mathematics.　All　Rights　Reserved.