Password-based authentications using smart cards are very necessary between login users and a remote server. Smart card security breach threatens the security of password-based authentication schemes with smart cards. A password-based authentication scheme with smart cards against smart card security breach was proposed by C.T. Li et al. recently. However, it is noted that Li et al.'s scheme needs a verification table in the remote server. A verification table should not be included in a good password-based authentication scheme. In this paper, based on hash functions, a secure password-based authentication scheme against smart card security breach and without maintaining verification tables is proposed, which improves the security of Li et al.'s scheme