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In view of the security threats faced by the vehicle-to-grid (V2G) network, this paper analyzes the V2G multi-domain network architecture and presents a network trust model suitable for the architecture. Based on the consortium blockchain, a cross-domain V2G authentication scheme is proposed, which achieves inter-domain user mutual authentication through the authentication between the domain user and the foreign domain server, and between the foreign domain server and its intra-domain users. The scheme utilizes the non-tampering characteristic of the blockchain, and adopts a hash algorithm in the digital identity verification to reduce the number of signatures and verifications in the scheme, thereby improving the efficiency and scalability of the scheme. The signature in the authentication scheme adopts the identity-based cryptographic algorithm SM9, and has the existence of unforgeable security under the adaptive selection message attack.