The long propagation delay in an underwater acoustic channel makes designing an underwater media access control (MAC) protocol more challenging. In particular, handshaking-based MAC protocols widely used in terrestrial radio channels have been known to be inappropriate in underwater acoustic channels, because of the inordinately large latency involved in exchanging control packets. Furthermore, in the case of multi-hop relaying in a hop-by-hop handshaking manner, the end-to-end delay significantly increases. In this paper, we propose a new MAC protocol named cascading multi-hop reservation and transmission (CMRT). In CMRT, intermediate nodes between a source and a destination may start handshaking in advance for the next-hop relaying before handshaking for the previous node is completed. By this concurrent relaying, control packet exchange and data delivery cascade down to the destination. In addition, to improve channel utilization, CMRT adopts a packet-train method where multiple data packets are sent together by handshaking once. Thus, CMRT reduces the time taken for control packet exchange and accordingly increases the throughput. The performance of CMRT is evaluated and compared with that of two conventional MAC protocols (multiple-access collision avoidance for underwater (MACA-U) and MACA-U with packet trains (MACA-UPT)). The results show that CMRT outperforms other MAC protocols in terms of both throughput and end-to-end delay.