The concept of group signature allows a group member to sign message anonymously on behalf of the group. In the event of a dispute, a designated entity can reveal the identity of a signer. Previous group signature schemes use an RSA signature based membership certificate and a signature based on a proof of knowledge (SPK) in order to prove the possession of a valid membership certificate. In these schemes, all of SPKs are generated over an unknown-order group, which requires more work and memory compared with a publicly-known-order group.In this paper, we present an efficient group signature scheme with a membership revocation function. Our membership certificate is based on a Nyberg-Rueppel signature (NR-signature) over a known-order group. We also reconstruct all SPKs that prove to have “valid” (non-revoked) membership certificate. As a result, our scheme is more efficient than another group signature based on NR-signature.