Abstract: Seamless roaming over wireless network is highly desirable to mobile users, and security such as authentication of mobile users is challenging. Recently, due to tamper-resistance and convenience in managing a password file, some smart card based secure authentication schemes have been proposed. This paper shows some security weaknesses in those schemes. As the main contribution of this paper, a secure and light-weight authentication scheme with user anonymity is presented. It is simple to implement for mobile user since it only performs a symmetric encryption/decryption operation. Having this feature, it is more suitable for the low-power and resource-limited mobile devices. In addition, it requires four message exchanges between mobile user, foreign agent and home agent. Thus, this protocol enjoys both computation and communication efficiency as compared to the well-known authentication schemes. As a special case, we consider the authentication protocol when a user is located in his/her home network.