With the rapid advances of the network technologies and mobile devices, users can easily use their mobile devices to access Internet services through wireless networks. In 2014, Kuo et al. proposed a mobility network authentication scheme and claimed their scheme was efficient and secure. Unfortunately, we find that their scheme has two weaknesses. First, it cannot resist man-in-the-middle attack. Second, it suffers from the synchronization problem in password change phase. In this study, the found weaknesses will be shown in detail, and an improved scheme for mobility networks is proposed to remedy these weaknesses. We also analyze the proposed scheme and prove that our scheme is secure and suitable for mobility networks.