In this paper, a Block Time Bounded Time Division Multiple Access (BTB-TDMA) medium access control (MAC) protocol is proposed for mobile underwater nodes (UNs) in underwater acoustic networks (UANets). The BTB-TDMA determines transmission schedule of UNs based on UNs' estimated propagation delays (EPDs), reflecting on UNs' mobility. Furthermore, the scheduling algorithm gives UNs time bound for data transfer with a unit of time block in order to reduce overall delay and avoid packet collisions among UNs. To analyze the protocol's performance, we divide BTB-TDMA into two cases, BTB-TDMA considering EPDs (BTB-TDMA1) and BTB-TDMA without considering EPDs (BTB-TDMA2), to show how the use of EPDs can improve overall network performance. In addition, we analytically derive the channel access delay and channel utilization of STUMP ( Kredo II et al., 2009) and TDMA, and compare them with those of BTB-TDMA. The numerical analysis shows that BTB-TDMA1 can reduce channel access delay by 20% and increase channel utilization by 35% at the maximum compared to those of BTB-TDMA2. BTB-TDMA2 provides at least 14% lower channel access delay and 37% higher channel utilization than STUMP. Furthermore, BTB-TDMA significantly outperforms TDMA, regardless of the network environment.