In group signature schemes, the members of a group can sign on a document on behalf of the group in such a way that the identity of the signer is not known to the verifier. But in case of dispute the identity of a particular member of the group can be identified. In this paper, we propose a braid groups based group signature scheme that imitates a real life situation in which each group member is equally important and there is no group leader. Our scheme keeps the identity of the signer anonymous. Security analysis shows that our group signature scheme is efficient and secure.