In the Vehicle-to-Grid (V2G) network, the electric vehicles (EVs) need to report their respective information, such as vehicle identity, battery capacity, battery state of charge (SoC), current location, and driving direction, to the power grid through the distributed local aggregators (LAGs), so that the power grid can dispatch power reasonably. However, the information has much to do with privacy of the EVs. The issue of how to solve the contradictory needs of privacy protection and information report is a challenging problem in the V2G network. This paper proposed a privacy preserving authentication mechanism together with a key exchange between the EVs and the LAGs, in which the EVs do not use any pseudonyms. Besides satisfying the requirements of anonymity, confidentiality, unlinkability, nonrepudiation, traceability and revocation, the scheme can further support forward security. The performance analysis shows that the proposed scheme is efficient in terms of computation and communication overhead. The experimental results show that the proposed scheme has fewer exchanged messages in the authentication process among compared schemes.