Vehicle-to-grid (V2G) technology has become a promising concept for the near future smart grid eco-system. V2G improves smart grid resiliency by enabling two-way communication and electricity flows while reducing the greenhouse gases emission. V2G practicality and stability is strongly based on the exchanged data between electrical vehicles (EVs) and the grid server (GS). However, using communication protocols to exchange vital information leads grid to being vulnerable against various types of attack. To prevent the well-known attacks in V2G network, this paper proposes a privacy-aware authentication scheme that ensures data integrity, confidentiality, users’ identity and location privacy, mutual authentication, and physical security based on physical unclonable function (PUF). Furthermore, the performance analysis shows that the proposed scheme outperforms the state-of-the-art, since EVs only use lightweight cryptographic primitives for every protocol execution.