In an electronic cash (e-cash) system, Recoverability means once you have lost your e-cash, you still can get back the amount of e-cash that you have lost. Untraceability means no one can trace where and when you have spent your e-cash. Obviously these are conflicting properties in an e-cash system. Most of the e-cash systems proposed in the literature do not include recoverability. Although some of them such as [17] contain recoverability, it is an on-line e-cash system. In this paper, we propose a new efficient e-cash protocol which possesses these two properties simultaneously. At the same time, it still remains off-line.