Abstract: 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.