Recently, Mun et al. analyzed Wu et al.'s authentication scheme and proposed a enhanced anonymous authentication scheme for roaming service in global mobility networks. However, through careful analysis, we find that Mun et al.'s scheme is vulnerable to impersonation attacks, off-line password guessing attacks and insider attacks, and cannot provide user friendliness, user's anonymity, proper mutual authentication and local verification. To remedy these weaknesses, in this paper we propose a novel anonymous authentication scheme for roaming service in global mobility networks. Security and performance analyses show the proposed scheme is more suitable for the low-power and resource-limited mobile devices, and is secure against various attacks and has many excellent features.