Vehicular ad hoc networks (VANETs) are fundamental components of building a safe and intelligent transportation system. However, due to its wireless nature, VANETs have serious security and privacy issues that need to be addressed. The conditional privacy-preserving authentication protocol is one important tool to satisfy the security and privacy requirements. Many such schemes employ the certificateless signature, which not only avoids the key management issue of the PKI-based scheme but also solves the key escrow problem of the ID-based signature scheme. However, many schemes have the drawback that the computational expensive bilinear pairing operation or map-to-point hash function are used. In order to enhance the efficiency, certificateless signature schemes for VANETs are usually constructed to support signature aggregation or online/offline computation. In this paper, we propose an efficient conditional privacy-preserving authentication scheme using an online/offline certificateless aggregate signature, which does not require bilinear pairing or map-to-point hash function, to address the security and privacy issues of VANETs. Our proposed scheme is proven to be secure with a rigorous security proof, and it satisfies all the security and privacy requirements with a better performance compared with other related schemes.