To eliminate the need of public-key certificates from Public Key Infrastructure (PKI) and the problem of key escrow in identity-based cryptography, the concept of self-certified public key was put forth by Girault. In this paper, we propose an efficient and novel self-certified signature scheme, which requires only one modular multiplication in signing with pre-computation. One of features of our scheme lies in its batch verification in both single-signer and multi-signer settings. Pairing computations in the batch verification are independent from the number of signatures. Our scheme is proven secure in the random oracle model. © 2012 Springer-Verlag Berlin Heidelberg.