Smart cities aim to improve the quality of life of citizens and efficiency of city operations through utilization of 5G communication technology. Based on various technologies such as IoT, cloud computing, artificial intelligence, and big data, they provide smart services in terms of urban planning, development, and management for solving problems such as fine dust, traffic congestion and safety, energy efficiency, water shortage, and an aging population. However, as smart city has an open network structure, an adversary can easily try to gain illegal access and perform denial of service and sniffing attacks that can threaten the safety and privacy of citizens. In smart cities, the global mobility network (GLOMONET) supports mobile services between heterogeneous networks of mobile devices such as autonomous vehicles and drones. Recently, Chen et al. proposed a user authentication scheme for GLOMONET in smart cities. Nevertheless, we found some weaknesses in the scheme proposed by them. In this study, we propose a secure lightweight authentication for roaming services in a smart city, called SLARS, to enhance security. We proved that SLARS is more secure and efficient than the related authentication scheme for GLOMONET through security and performance analysis. Our analysis results show that SLARS satisfies all security requirements in GLOMONET and saves 72.7% of computation time compared to that of Chen et al.’s scheme.