Group signature has a wide application in the field of electronic business and politics. Lots of variant group signature schemes have been invented in the last 15 years. Among them, some research papers are about the group signature itself, which means that new group signature schemes are to be constructed based on find new intractable assumptions; some papers are about the combination of blind signature and group signature, called group blind signature schemes; some papers are about the combination of forward secure signature and group signature, called forward secure group signature schemes. But there is no research papers about the group signature scheme with authorization. In this paper, a new kind of group signature scheme with authorization is constructed based on the BMW's scheme, which is a group signature scheme whose security is based on the standard assumption. Compared with BMW's scheme: Adding authorization generation algorithm to key generation algorithm in group signature scheme, although the speed of instance production of group signature scheme slows down, strengthens group signature scheme with authorization characteristic, which promotes group signature application in electronic business and electronic politics; and furthermore, the proof of theorem 2 in this paper is simpler than that of BMW's scheme.