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It is important for security of satellite mobile communication networks to design an efficient access authentication process. A two-way access authentication scheme among mobile users, gateways and the Network Control Centre (NCC) is designed in this study. The authentication scheme consists of four phases: mobile users registration, mobile users management, mobile authentication and mobile authentication update. Furthermore, the Syverson-van Oorschot (SVO) logic is introduced to reason the authentication scheme to verify the security. This scheme highlights the authentication role of gateways, and decreases the authentication computation load of the NCC. The access authentication scheme can resist attacks from any side, including the identity spoofing, tampering, replay etc. The integrity of the transmission data is also protected. Therefore the security for satellite mobile communication networks is enhanced. This access authentication scheme is implemented on the developed satellite mobile communication simulation platform. The obtained simulation results suggest that the authenticated overheads for audio service and video service are low, and the proposed scheme does not degrade the quality of service (QoS) of the satellite mobile communication.