To address the efficiency issues of vehicle identity authentication schemes based on cryptographic primitives in vehicular networks, a novel lightweight identity authentication and key agreement protocol based on Physical Unclonable Functions (PUFs) is proposed. The proposed protocol authenticates identities by generating Challenge-Response Pair (CRP) data in real time, avoiding the privacy leaks and security risks associated with traditional PUF authentication, which relies on the verifier's pre-stored CRP data. Additionally, the proposed protocol eliminates the use of complex cryptographic primitives and digital certificates in the authentication process, thereby reducing the computational and communication overhead for verifiers and the trusted authority, significantly enhancing authentication efficiency. The security analysis shows that the protocol not only protects the real identities of vehicles but also provides traceability of malicious identities, effectively defending against various security threats, including physical cloning and replay attacks. Compared to cryptographic-based identity authentication protocols, this lightweight protocol is better suited for resource-constrained and latency-sensitive vehicular network environments.