Rational secure two-party computation (RSTPC) applies game theory to cryptographic protocols, where rational parties only care about how to maximize their utilities. Fairness can be achieved by assuming rational behavior in RSTPC. Previous RSTPC protocols achieve fairness under symmetric information, which seems quite strong and unnatural for rational parties. In this paper, we consider a general RSTPC protocol under asymmetric information where previous equilibriums are inadequate to guarantee fairness. Therefore, we propose a stronger equilibrium named computationally sequential equilibrium to guarantee fairness under asymmetric information. Furthermore, our protocol only requires small constant communication rounds. Copyright © 2014 John Wiley & Sons, Ltd.