In vehicular networks, vehicles should be able to authenticate each other to securely communicate with networkbased infrastructure, and their locations and identifiers should not be exposed from the communication messages. However, when an accident occurs, the investigating authorities have to trace down its origin. As vehicles communicate not only with RSUs(Road Side Units) but also with other vehicles, it is important to minimize the number of communication flows among the vehicles while the communication satisfies several security properties such as anonymity, authenticity, and traceability. In our paper, when the mutual authentication protocol is working between vehicles and RSUs, the protocol offers the traceability with privacy protection using pseudonyms and MAC (Message Authentication Code) chain. And by using MAC-chain as one-time pseudonyms, our protocol does not need a separate way to manage pseudonyms.