Internet of vehicles (IoVs) is a variant of vehicular ad-hoc network, which provides an efficient communication method for vehicles. However, some traffic messages usually include sensitive identity information, which is easy to bring about the leakage of vehicular identities during data communications. Further, if vehicular identities are fully protected, then it can lead to trusted authority cannot reveal the real identities of malicious vehicles, which incurs more security issues in IoVs. Therefore, in this paper we propose an efficient conditional identity privacy-preserving authentication scheme based on cooperation of multiple fog servers under fog computing-based IoVs, where fog servers are used to verify (authenticate) the legitimacy of vehicles without revealing their real identities. Further, an associated vehicular identity updating mechanism is constructed to solve that some compromised fog servers may leak their stored verification information to pool real vehicular identities. Additionally, a malicious vehicular identity tracing mechanism is proposed to support related fog servers that receive signed false messages can trace the real identities of malicious vehicles. Compared with other related schemes, our scheme further improves its security. Experimental results show our scheme is efficient under fog computing-based IoVs.