In global mobile network, it is required to authenticate mobile users, provide secure communication channel be- tween a user and a foreign agent using session key, and guarantee users' anonymity and untraceability. In order to improve the security of mobile roaming service, two- factor authentication which employs smart card and pass- word was introduced to global mobile network. In 2014, Kuo et al. [5] proposed an anonymous two-factor authentication scheme for mobile roaming service. However, we found that this scheme is vulnerable to four kinds of manin-the-middle attacks and denial-of-service attack. In this paper, we first review Kuo et al.'s scheme and analyze its weaknesses. Then, we propose an efficient anonymous two-factor authentication protocol that overcomes those vulnerabilities in Kuo et al.'s.