In order to solve complex algorithm and high time delay for vehicle-to-vehicle(V2V) communication in 5G vehicle-to-everything(V2X), an anonymous V2V authentication and key agreement protocol based on physical unclonable function(PUF) is proposed. By using lightweight PUF, vehicles can avoid digital signature, key storage and certificate escrow to reduce the overhead of calculation and storage. At the same time, our protocol only needs one-way communication between two vehicles and 5G service network(SN) and one handshake communication between two vehicles to complete V2V authentication and key agreement scheme, which can greatly reduce the communication overhead and time delay. What’s more, PUF binds the on board unit(OBU) of vehicle to the 5G SIM card, which can resist identity forgery attacks. Through the construction of identity index table, the regulatory authority can track the source of vehicles’ pseudo identities through 5G SN, which satisfies conditional anonymity. The security of the proposed protocol is proved in the Dolve-Yao model by AVISPA which is a formal analysis tool. Also, it is superior to the existing 5G V2X anonymous communication protocols in terms of computation overhead, communication overhead and security. Our protocol can provide essential security for V2V communication in 5G V2X.