The on-line electronic payment system has been criticized mostly for its cost inefficiency and its inconvenience. However, with the fast development of mobile technology, the world has been changed. People nowadays like to carry their mobile telephone with them. It is very convenient for them to connect to the Internet anytime and anywhere and the cost of mobile communication is dropping very fast. This paper introduces an electronic payment system that implements Brands' (1994, 1995) restrictive blinding signature into the user's mobile telephone or user's PDA. The system is very efficient and offers multi-party security as well as unconditional privacy of payments. Our system has some features of the on-line system, so it can prevent double-spending from happening.