In　this　paper,　we　propose　a　single　species　logistic　model　with　feedback　control　and　additive　Allee　effect　in　the　growth　of　species.　The　basic　aim　of　the　paper　is　to　discuss　how　the　additive　Allee　effect　and　feedback　control　influence　the　above　model’s　dynamical　behaviors.　Firstly,　the　existence　and　stability　of　equilibria　are　discussed　under　three　different　cases,　i.e.,　weak　Allee　effect,　strong　Allee　effect,　and　the　critical　case.　Secondly,　we　prove　the　occurrence　of　saddle-node　bifurcation　and　transcritical　bifurcation　with　the　help　of　Sotomayor’s　theorem.　The　above　dynamical　behaviors　are　richer　and　more　complex　than　those　in　the　traditional　logistic　model　with　feedback　control.　We　find　that　both　Allee　effect　and　feedback　control　can　increase　the　species’　extinction　property.　We　also　reveal　some　new　bifurcation　phenomena　which　do　not　exist　in　the　single-species　model　with　feedback　control　(Fan　and　Wang　in　Nonlinear　Anal.,　Real　World　Appl.　11(4):2686–2697,　2010　and　Lin　in　Adv.　Differ.　Equ.　2018:190,　2018).　©　2020,　The　Author(s).