RFID system is a technique to obtain information of tag using radio frequency. Specificity of RFID systems using radio frequency has many problems that is eavesdropping, location tracking, spoofing attack, replay attack, denial of service attack. So, RFID protocol should be used cryptographic methods and mutual authentication for security and privacy. In this paper, we explain the problem of past protocol and propose the nonfixed symmetric key-based RFID mutual authentication protocol using shift computation and random number. Proposed protocol is secure from various attacks. Because it use shift operation and non-fixed symmetric key.