Abstract: In the setting of traditional secure two-party computation, one party may either tell a wrong output to the other party or abort the protocol after he obtains the computation output. So, completed fairness can not be achieved. To address this problem, combining game theory with cryptography, a rational secure two-party computation protocol is proposed in this paper. Firstly, we suppose that any rational party would prefer getting the computation output to not getting it and secondly, it is preferred that as few as possible of the other players get it. Then, game strategies, utilities, and motivations that participants deviate from the protocol or abide by the protocol are researched, and a game model for secure two-party computation is constructed. In the protocol, it is a best strategy for parties to abide by the protocol. The cheating of party can be detected and the gain of the following the protocol is more than the gain of deviating, so rational party has incentive to abiding by the protocol. Finally, every party can obtain the computation result. Analysis shows that the protocol is secure and fair.