Wireless communications have become one of the most key parts in our everyday life, which give us facility on work and life but they still bring a great security risk. A crucial problem with wireless communications is to ensure the security of communication and prevent the privacy of communication entities revealing. Authentication is becoming an important issue when a mobile user (MU) wants to access services provided by the home agent (HA) in a visited foreign agent (FA). Recently, Kuo et al. proposed an authentication scheme and claimed that the proposed scheme was secure against different kinds of attacks. In this paper, we show that Kuo et al.'s scheme fails to resist insider and verifier attacks while it does not provide local verification. In addition, password change phase of Kuo et al.'s scheme also has a loophole. To remedy these shortcomings, an improved anonymous authentication scheme for wireless communications is proposed which is immune to various known types of attacks. Finally, in comparison with other existing schemes regarding security properties and performance, we show that our scheme has various kinds of security properties and is suitable for practical applications in wireless networks.