A micropayment scheme provides a secure and efficient solution for electronic payment environments that require frequent transactions with nominal fees. It is particularly suitable for mobile applications in which a customer is charged for either time spent or data volume transferred. Most proposed micropayment schemes are based on “PayWord” by Rivest and Shamir. The security and efficiency of a micropayment scheme can be ensured by adopting the hash chain technique. Recent research on micropayment has introduced additional properties such as user anonymity and fairness. However, the existing schemes may lose efficiency and some of the original desirable properties of PayWord while achieving new ones. We propose an anonymous fair offline micropayment scheme that satisfies user anonymity and fairness and retains the efficiency and properties of PayWord, such as offline broker. A user can make multiple purchases from different vendors without interacting with the broker again. PayWord's postpaid mechanism is adopted in order to make our scheme more attractive to users. To the best of our knowledge, this is the first micropayment scheme to simultaneously offer the aforementioned properties. Copyright © 2012 John Wiley & Sons, Ltd.