Vehicle-to-Grid (V2G) networks have emerged as a new communication paradigm between Electric Vehicles (EVs) and the Smart Grid (SG). In order to ensure seamless communications between mobile EVs and the electric vehicle supply equipment, the support of ubiquitous and transparent mobile IP communications is essential in V2G networks. However, enabling mobile IP communications raises real concerns about the possibility of tracking the locations of connected EVs through their mobile IP addresses. In this paper, we employ certificate-less public key cryptography in synergy with the restrictive partially blind signature technique to construct a secure and privacy-aware proxy mobile IPv6 (SP-PMIPv6) protocol for V2G networks. SP-PMIPv6 achieves low authentication latency while protecting the identity and location privacy of the mobile EV. We evaluate the SP-PMIPv6 protocol in terms of its authentication overhead and the information-theoretic uncertainty derived by the mutual information metric to show the high level of achieved anonymity.