In recent years, the global mobility networks have grown rapidly and significantly and the smart phones have become practical and even vital tools for users. Furthermore, the roaming service of smart phones provides a possibility for users to share their information with others outside of the geographical region of home agent with the aid of foreign agent. In this paper, first, we prove that the previously-published schemes in this field not only are vulnerable to some known attacks, such as the reply attack, insider attack, user, home agent, and foreign agent impersonation attacks, and Denial of Service attack, but also some security features such as user anonymity, untraceability, mutual authentication, perfect forward secrecy, and session key security are not provided. Second, an authentication scheme based on smart card is presented for the global mobility networks, which not only can solve the security weaknesses of the previous schemes, but also can provide the anonymity and mutual authentication between the three entities of user, home agent, and foreign agent. Finally, security and efficiency of the proposed scheme are compared with the previously-proposed schemes. The results demonstrate that the proposed scheme provides a proper level of both security and efficiency.