In 2009, Kim-Chung proposed a secure remote user authentication scheme. In this paper, we show that Kim-Chung’s scheme does not establish a session key. Moreover, the scheme requires time-synchronisation. In order to remedy these drawbacks, this paper proposes an improvement scheme which fulfils all the security requirements for a remote user authentication scheme. Security analysis proved that the improved scheme resists the typical attacks. Furthermore, the analysis of computational cost and storage capacity demonstrated that the scheme is feasible for a practical implementation.