A　nonautonomous　discrete　two-species　competition　system　with　infinite　delays　and　single　feedback　control　is　considered　in　this　paper.　Based　on　the　discrete　comparison　theorem,　a　set　of　sufficient　conditions　which　guarantee　the　permanence　of　the　system　is　obtained.　Then,　by　constructing　some　suitable　discrete　Lyapunov　functionals,　some　sufficient　conditions　for　the　global　attractivity　and　extinction　of　the　system　are　obtained.　It　is　shown　that,　by　choosing　some　suitable　feedback　control　variable,　one　of　two　species　will　be　driven　to　extinction.