In　order　to　solve　the　problem　of　exceeding　authority　signature　and　the　anonymity　of　the　authorized　group　signature　that　often　appears　in　electronic　commerce　and　electronic　governance,　this　paper　proposes　a　secure　authorized　group　signature　scheme　based　on　the　discrete　logarithm.　In　this　scheme,　authors　add　a　right　manager,　and　make　him　issue　the　corresponding　authorized　certificate　to　the　appointed　group　member,　and　an　open　certificate　to　the　group　manager.　It　enables　every　member　of　the　group　to　make　a　signature　under　his　purview,　and　it　solves　the　problem　of　exceeding　authority　signature　that　often　appears　in　electronic　commerce　and　electronic　governance.　Simultaneously,　using　the　knowledge　of　number　theory,　it　can　guarantee　the　anonymity　of　the　authorized　group　signature.