Universal roaming is one kind of service provided in global mobility networks (GLOMONET). User authentication is an important topic for the roaming service. In this article, we propose a novel user authentication scheme for GLOMONET. The proposed scheme uses only one-way hash functions and smart cards to achieve the purpose of security, and it provides for mobile users the feature of anonymity. Besides, it not only avoids the possible attacks appeared in existing methods but also needs low computation cost for mobile communications.