Mutual authentication scheme plays a significant role in the global mobility network to afford roaming service. However, designing secure and privacy-preserving authentication protocols for roaming service is always challenging. Due to the nature of wireless communication medium, these networks are vulnerable to security threats. In recent times, some authentication systems have been proposed for the mobile user roaming in the mobility environments. Nevertheless, most of the security protocols are prone to security attacks. In this paper, a secure mutual authentication protocol is designed using lightweight cryptographic primitives. The protocol design includes initialization phase, registration phase, mutual authentication phase, and the password change phase to ensure the user anonymity, privacy, and security in global mobility networks. In addition, we used a popular formal verification tool called AVISPA (Automated Validation of Internet Security Protocols and Applications) to check the correctness of the proposed protocol. Notably, the formal security analysis has been carried out through BAN logic, which proves the security strength of the proposed framework. Finally, a performance analysis shows that the proposed authentication system preserves low computational and communication overheads.