Information security problem has become one of the hottest issues in RFID system. More and more researchers begin to study how to provide security protection in the RFID system. In the paper, we mainly research lightweight authentication protocols in RFID system. Firstly, we analyze some protocols. Secondly, we introduce a serverless authentication protocol for RFID system and analyze its security. We find it does not provide forward security. Thirdly, we propose a revised serverless authentication protocol with forward security. It provides two-way authentication and privacy protection, resists tracking and cloning attack as well as the original protocol. Moreover, it provides forward security protection and resists desynchronization attack. For the efficiency, its computational complexity is at the same level with the protocol proposed by Tan et al.