The concept of the Social Internet of Things (SIoT) can be viewed as the integration of prevailing social networking and the Internet of Things, which is making inroads into the daily operation of many industries. Smart grids, which are cost-effective and environmentally friendly applications, are a promising field of the SIoT. However, security and privacy concerns are the dark aspects of smart grids. The goal of this paper is to address the security and privacy issues in the vehicle-togrid (V2G) networks with the intention of promoting a more extensive deployment of V2G networks for smart grids. Driven by this motivation, in this paper, we propose a robust key agreement protocol that can achieve mutual authentication without exposing the real identities of users. Efficiency is also a major concern in resource-constrained environments. By leveraging only hash functions and bitwise exclusive-OR operations, the proposed protocol is highly efficient compared with pairing-based protocols. In addition, we define a formal security model for our privacy-preserving key agreement protocol for V2G networks. Using this model, a formal security analysis shows that the proposed protocol is secure. Moreover, an informal security analysis demonstrates that our protocol can withstand different types of attacks.