Authentication and privacy-preserving are two important security properties for a cryptographic protocol for RFID tags. However, providing privacy-preserving often increases the cost of looking up a tag in the database. In response to this issue, Ryu and Takagi proposed an RFID authentication protocol which provides a way to trade-off security and memory for performance. In this paper, we first point out that Ryu and Takagi's protocol does not provide any privacy-preserving at all. We then propose a solution to achieve privacy-preserving in Ryu-Takagi protocol.