To design a mobile user authentication protocol with anonymity for the global mobile network is a challenge, since wireless network is more vulnerable to attacks and mobile terminals’ computational power is limited. In 2012, Li & Lee proposed a user authentication and privacy preserving scheme with smart card for wireless communications. In this paper, we improve the adversary model of this type of authentication scheme, and then demonstrate that Li & Lee’s scheme is vulnerable to off-line password guessing attack. To remedy this security weakness, an improved scheme is proposed, which is more efficient than Li & Lee’s scheme.