Lee and Kwon proposed an anonymous authentication scheme based on Zhu et al.'s scheme. However, Lee et al.'s scheme has two disadvantages. Firstly, their scheme is vulnerable to off-line dictionary attacks. An adversary can guess a user password from the user's login messages eavesdropped by the adversary. Secondly, an authentication server called a home agent requires a verification table, which violates the original advantage of Zhu et al.'s scheme. That is, it increases the key management costs of the home agent. In this letter, we show the weaknesses of Lee et al.'s scheme and another three existing schemes. Then, we propose a new secure scheme without the verification table, while providing security for off-line dictionary attacks and other attacks except for a certain type of combined attacks.