Designing a pragmatic medium access control (MAC) protocol to operate at low collision rate while providing high throughput is significant for underwater acoustic networks (UANs). Though the centralized control approach could greatly reduce transmission collisions, it normally requires the real-time global network information, such as traffic load, remaining energy, network topology, etc., which is a harsh requirement especially in dynamic UANs. In contrast, the distributed control scheme appears to be more attractive and promising. However, due to the long propagation delay of acoustic signals in the water, the spatiotemporal uncertainty problem and the carrier sensing zone problem in UANs make the distributed MAC protocol unable to avoid frame collisions effectively, which degrades the network performance. For this, we propose an MAC protocol, called FCFS, using the First-Come-First-Served basis, which achieves low frame collision and high network throughput in UANs by adopting the mechanism of medium access reservation via an advance handshaking. Different from the traditional handshake-based protocols, FCFS is good at handling the hidden terminal problem by considering the complete exchange of channel access information among neighboring nodes. Simulation results confirm that the proposed protocol could improve the data reception rate and throughput compared to the related protocols. It also shows that our proposed scheme could maintain a stable performance under different network traffic loads.