Vehicular Ad-hoc NETwork （VANET） is vital for constructiong intelligent transportation systems because of obvious advantages in sharing traffic data， improving driving efficiency and reducing traffic accidents. Meanwhile， problems such as secure communication of vehicle-to-vehicle and vehicle-to-infrastructure， privacy-preserving of vehicles （e.g.， identity privacy， location privacy）， and efficient authentication of traffic messages need to be solved urgently. To achieve a trade-off between security and efficiency， firstly， the recently proposed scheme， namely Conditional Privacy-Preserving CertificateLess Aggregate Signature scheme （CPP-CLAS）， was analyzed and proved to be unable to resist the public key replacement attack. Then， based on this scheme， a new certificateless conditional privacy-preserving authentication scheme for VANET was proposed， in which the secure channels were not required during partial private key generation of vehicles. In addition， aggregate verification and batch verification were employed to verify a batch of signatures in the scheme. Finally， the proposed scheme was proved to have unforgeability under random oracle model. Performance analysis show that compared with the similar schemes， the proposed scheme improves the computational efficiency of the signature phase by at least 66.76% and reduces the communication bandwidth demand by at least 16.67% without increasing the verification overhead， verifying that the proposed scheme is more suitable for resource-constrained VANET.