RFID system is used in several fields such as traffic and access control. The study about RFID security is actively progressed as security threat has been increased. This paper suggests matrix-based authentication protocol. And we analyze the safety of authentication protocol and compares the effectiveness of the protocol with other authentication protocols. The suggested authentication protocol secures from wiretapping attack, replay attack, and spoofing attack, and reduces overload of back-end database so that has efficient performance.