In this paper we propose a secure and efficient off-line micro payment scheme. There are five parties in our scheme: Consumer, Bank, Merchant, Issuer and Trusted Authority. The coins are made by Bank in cooperation with Issuer to prevent not only Bank from impersonating a consumer to steal consumer's money but also Issuer from making coins of his own accord. The representation of coins is based on hash chain technique that the coin verification can be done quickly during a transaction. Furthermore, we propose a dual signature scheme extended from RSA algorithm that a legitimate coin must be signed by both Issuer and Consumer to assure no one except Consumer can spend coins, and no coin can be expanded from any legitimate coin chain. In summary, our system has the following properties: (1) Unforgeability and Unexpandability of coins. (2) Efficiency of coins verification. (3) No-usurpation of coins. (4) Anonymity of Consumer. (5) Traceability of double-spender.