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Underwater acoustic sensor networks (UWSN) have attracted a lot of attention recently. The long propagation delay of acoustic signals in UWSN causes spatial-temporal uncertainty making spatial fairness in UWSN a challenging problem. Time of arrival of the packets depends on both the sending time and the distance between the transmitter and the receiver. Hence, it is difficult to avoid collision and guarantee the fairness of transmission in underwater environment. In this paper, we propose a spatially fair multiple access control (SF-MAC) protocol called SF-MAC in UWSN. The SF-MAC can avoid collision by postponing the clear-to-send frame equal to period of request-to-send (RTS) contention period. The receiver collects RTSs from all the contenders during the RTS contention period and calculates the potential sending time of each of contender. It determines the earliest transmitter with a probability rule that compares with the first RTS. In case of multiple contenders, the SF-MAC can maintain a more exact order of transmission to achieve fairness of transmission. Finally, we present a comprehensive performance study via simulations. The results show that SF-MAC can perform better than existing MAC schemes (such as MACA, MACA-U, and T-Lohi) in terms of the spatial fairness and network throughput.