With the development of the Internet, the 5th generation (5G) of mobile communication technology emerges. The 5G authentication and key agreement (5G-AKA) protocol is proposed mainly to achieve two-way authentication between users and service networks. However, recent research suggests that the protocol may be subject to information deciphering and message replay attacks. At the same time, it is found that some variants of the current 5G-AKA cannot satisfy the protocol’s unlinkability. Therefore, in response to these shortcomings, this study proposes an improvement plan called SM-AKA. SM-AKA is composed of two parallel sub-protocols in a novel way. In addition, through the flexible mode switching, lightweight sub-protocols (GUTI submodule) are frequently adopted, and the other sub-protocol (SUPI submodule) is used to deal with abnormalities caused by authentication. Therefore, this mechanism not only realizes the efficient authentication between users and networks but also improves the stability of the protocol. Furthermore, the freshness of variables has been effectively maintained to prevent the replay of messages, and strict encryption and decryption methods have further strengthened the security of the protocol. Finally, the study carries out a complete evaluation of SM-AKA. Through formal modeling, attack assumptions, and Tamarin derivation, it is proved that the plan can achieve the authentication and privacy goals, and the theoretical analysis has demonstrated the performance advantage of the protocol.