Certificate-based cryptography optimizes certificate management of the traditional public key infrastructure (PKI) and overcomes the problems of the key escrow and the key distribution in identity-based cryptography (IBC). Currently, many certificate-based signature (CBS) schemes have been proposed in the random oracle model or standard model. However, all existing schemes in the standard model are quietly inefficient. In this paper, we propose an efficient certificate-based signature over bilinear groups in the standard model. Compared with the state-of-the-art constructions in the standard model, the proposed scheme is superior in both communication cost and computational overhead.