Underwater acoustic sensor networks (UASNs) use wireless acoustic signals for communication and are widely used in resource monitoring, environmental protection, etc. The characteristics of UASNs, such as long propagation delay, narrow bandwidth, and limited energy, bring great challenges to MAC protocol design. However, the long propagation delay also creates opportunities for multiple node pairs to achieve parallel transmission. In this paper, a parallel-transmission MAC protocol for distributed UASNs is proposed. Based on the existing random time slot MAC protocol, the proposed protocol exploits the location information of node pairs to achieve collision-free parallel transmission. Moreover, an extra sleeping mechanism is designed for nodes so as to reduce energy consumption. Compared with the previous MAC protocol, simulation results show the superiority of the proposed MAC protocol in terms of network throughput, average energy consumption and delivery rate.