There is an advantage that RFID system is better than previous bar code system in storage ability and noncontact property. But, everyone can easily receive the transmitting information by using RF signal. So, there is a problem that system security and personal privacy are threatened. In this paper, I propose RFID system that is secure against attacks like eavesdropping, replay, spoofing and location tracking and can efficiently provide mutual authentication services between reader and tag. The proposed RFID system can be used in various sections of ubiquitous computing environment.