In global mobility networks, anonymous user authentication is an essential task for enabling roaming service. In a recent paper, Jiang et al. proposed a smart card based anonymous user authentication scheme for roaming service in global mobility networks. This scheme can protect user privacy and is believed to have many abilities to resist a range of network attacks, even if the secret information stored in the smart card is compromised. In this paper, we analyze the security of Jiang et al.'s scheme, and show that the scheme is in fact insecure against the stolen-verifier attack and replay attack. Then, we also propose a new smart card based anonymous user authentication scheme for roaming service. Compared with the existing schemes, our protocol uses a different user authentication mechanism, which does not require the home agent to share a static secret key with the foreign agent, and hence, it is more practical and realistic. We show that our proposed scheme can provide stronger security than previous protocols.