We　propose　and　study　a　class　of　discrete-time　commensalism　systems　with　additive　Allee　effects　on　the　host　species.　First,　the　single　species　with　additive　Allee　effects　is　analyzed　for　existence　and　stability,　then　the　existence　of　fixed　points　of　discrete　systems　is　given,　and　the　local　stability　of　fixed　points　is　given　by　characteristic　root　analysis.　Second,　we　used　the　center　manifold　theorem　and　bifurcation　theory　to　study　the　bifurcation　of　a　codimension　of　one　of　the　system　at　non-hyperbolic　fixed　points,　including　flip,　transcritical,　pitchfork,　and　fold　bifurcations.　Furthermore,　this　paper　used　the　hybrid　chaos　method　to　control　the　chaos　that　occurs　in　the　flip　bifurcation　of　the　system.　Finally,　the　analysis　conclusions　were　verified　by　numerical　simulations.　Compared　with　the　continuous　system,　the　similarities　are　that　both　species＇　densities　decrease　with　increasing　Allee　values　under　the　weak　Allee　effect　and　that　the　host　species　hastens　extinction　under　the　strong　Allee　effect.　Further,　when　the　birth　rate　of　the　benefited　species　is　low　and　the　time　is　large　enough,　the　benefited　species　will　be　locally　asymptotically　stabilized.　Thus,　our　new　finding　is　that　both　strong　and　weak　Allee　effects　contribute　to　the　stability　of　the　benefited　species　under　certain　conditions.