In vehicle to grid (V2G), electric vehicles face the risk of privacy leakage when performing cross-domain authentication because of the openness and instability of mobile network. Although the existing conditional anonymous authentication schemes can both protect the vehicles' anonymity and trace the vehicles' real identity in case of malicious behaviors, the commonly used group signature and ring signature methods have limitations, such as high costs. Therefore, how to effectively apply conditional anonymous authentication in the V2G cross domain scenario to meet the high real-time requirements of V2G has become a key challenge. To address this challenge, we propose innovatively an efficient multi-level and cross-domain conditional anonymous authentication scheme in V2G. The scheme designs a unique multi-level architecture. The first level faces grid servers and uses the group signature whose group key is generated based on the Chinese Remainder Theorem for grid servers, and the second level faces vehicles and uses the proxy signature to generate conditional anonymous cross-domain signatures for vehicles. To further improve efficiency, our scheme also uses the online/offline signature. Thus, our scheme has less computational, communication, and storage costs compared to existing schemes. Through formal security model and analysis, the security of the proposed scheme is shown.