With the popularization of the networking, the network payments have become a trend. Electronic cash (e-cash) is such kind of payment; however, although various types of the demands in e-cash implementations have been conceived of, an e-cash scheme with fairness property has not yet been proposed. In this article, we present a novel electronic cash model, which uses a verifiable encryption and a restrictive blind signature to construct an electronic cash system with fairness between customers and merchants. The proposed e-cash scheme properly combines the payment protocol with a fair exchange procedure, so that the customer and the merchant can fairly exchange their money and goods. Our scheme can maintain fairness with the aid of an off-line trusted third party (off-line TTP). That means in a normal case, the customer and the merchant can receive their desired items without TTP's participation. However, only when a dispute occurs, the TTP can help both parties resolve the problem and ensure the fairness of the transaction. Moreover, this system can also protect customers privacy, and prevent some hostile deceptions such as double spending and stealing. The system has also been implemented in a PDA emulator for wireless communications to evaluate the efficiency of running the program on a low computing power device.