Compared to a terrestrial communication, the high BER(Bit Error Ratio) and low channel bandwidth are the major factor of throughput degradation due to characteristics of underwater channel. Therefore, a MAC protocol must be designed to solve this problem in UWASNs(Underwater Acoustic Sensor Networks). MAC protocols for UWASNs can be classified into two major types according to the contention scheme(Contention-free scheme and Contention-based scheme). In large scale of sensor networks, a Contention-based scheme is commonly used due to time-synchronize problem of Contention-free scheme. In the contention-based scheme, Each node contends with neighbor nodes to access network channel by using Back-off algorithm. But a Slot-Time of Back-off algorithm has long delay times which are cause of decrease network throughput. In this paper, we propose a new scheme to solve this problem. The proposed scheme uses variable Slot-Time instead of fixed Slot-Time. Each node measures propagation delay from neighbors which are used by Slot-time. Therefore, Slot-Times of each node are optimized by considering node deployment. Consequently, the wasted-time for Back-off is reduced and network throughput is improved. A new mac protocol performance in throughput and delay is assessed through NS3 and compared with existing MAC protocol(MACA-U). Finally, it was proved that the MAC protocol using the proposed scheme has better performance than existing MAC protocol as a result of comparison.