With the rapid development of computing technology, traditional cryptographic systems based on numbertheoretic problems are facing severe security threats. Therefore, Vehicle-to-grid (V2G) as a fundamental part of the smart grid (SG) urgently needs to design secure authentication and key negotiation protocols that can resist such emerging attacks. We have identified several security vulnerabilities in Yu et al. protocol, such as password hacking, secret leakage, user impersonation, and charging station impersonating attacks, etc. These findings may be useful for future research on designing secure authentication schemes.