A group signature scheme introduced by Chaum and Van Heyst allows a group member to sign messages anonymously on behalf of the group. However, in the case of a dispute, the identity of a signer of a group signature can be revealed only by a privileged entity, called a group manager. The group signature scheme has mainly been studied from the viewpoint of computational security setting so far. The main contribution of this paper is to study group signature schemes in unconditional security. More specifically, we newly introduce strong security notions of unconditionally secure group signatures (USGS for short) based on the idea of those of computationally secure group signatures proposed by Bellare, Micciancio and Warinschi. We also provide a generic method to construct USGS that is provably secure in our security definition. More precisely, we construct USGS by combining an encryption scheme with a signature, and show that the constructed scheme is unconditionally secure if the encryption and the signature used in the construction are unconditionally secure. Finally, we provide an instantiation of the one-time secure group signature scheme based on the generic construction.