Abstract—It is becoming much significant in the security of password-based authentication over the Internet. Recently, with a formal proof, the improved anonymous passwordbased authentication scheme was proposed by Wu, Chen, and Wang. Within the practical applications, the scheme provides better performance for security. The scheme has claimed the ability to withstand various known attacks, such as user anonymity, user and server impersonations, and so on. Unfortunately, there still exist some weaknesses in the scheme. This work shows that the scheme is not secure to those attacks, such as online password guessing and denial of service attacks. Finally, the improved scheme is proposed.