Underwater acoustic sensor network (UWASN) has recently aroused the interest of researchers and scientists in this field. The acoustic sensor bandwidth is limited in underwater and it causes low successful packet transmission. One of the methods to overcome this handicap is efficient broadcast scheduling of underwater acoustic sensor node (UASN) that would help in transmitting and receiving data without any collision. This can be done with the help of time division multiple access (TDMA). The basic idea is to address broadcast scheduling problem in UWASN for utilizing the limited available bandwidth by parallelizing the node transmission such that it does not interfere with each other in same time slot; it also minimizes the node turnaround transmission time in the network by optimizing the time slots in TDMA frame. The objective of this paper is to maximize the utilization of the available underwater acoustic bandwidth and to achieve high throughput as well as to reduce the node turnaround wait time by using an evolutionary genetic algorithm (GA). The simulation results prove that every node in the UWASN transmits in an average minimal turnaround time by minimizing the time slots and maximizing the throughput in the network by scheduling the possible nodes with parallel transmission. © 2018, Springer-Verlag London Ltd., part of Springer Nature.