Authenticated Diffie-Hellman key agreement is quite popular for establishing secure session keys. As resource-limited mobile devices are becoming more popular and security threats are increasing, it is desirable to reduce computational load for these resource-limited devices while still preserving its strong security and convenience for users. In this paper, we propose a new smart-card-based user authenticated key agreement scheme which allows users to memorize passwords, reduces users’ device computational load while still preserves its strong security. The proposed scheme effectively improves the computational load of modular exponentiations by 50%, and the security is formally proved. Authenticated Diffie-Hellman key agreement is quite popular for establishing secure session keys. As resource-limited mobile devices are becoming more popular and security threats are increasing, it is desirable to reduce computational load for these resource-limited devices while still preserving its strong security and convenience for users. In this paper, we propose a new smart-card-based user authenticated key agreement scheme which allows users to memorize passwords, reduces users’ device computational load while still preserves its strong security. The proposed scheme effectively improves the computational load of modular exponentiations by 50%, and the security is formally verified.