A t-out-of-n threshold group signature is a generalization of group signature, in which only t or more members from a given group with n members can represent the group to generate a signature anonymously and the identities of the participating signers can be revealed in case of a dispute later. A new approach to convert any threshold signature into a threshold group signature is proposed in this paper. Compared with the proposal presented by Petersen, our approach has better efficiency and shorter signatures, and it does not require any secure channel among the participating signers. In particular, when the interpolation coefficients are calculated by the group manager, it has better anonymity.