Underwater acoustic sensor networks (UASNs) are critical to a range of applications from oceanographic data collection to submarine surveillance. In these networks, efficient energy management is critical due to the limited power resources of underwater sensors. The LEACH protocol, a popular cluster-based protocol, has been widely used in UASNs to minimize energy consumption. Despite its widespread use, the conventional LEACH protocol faces challenges such as an unoptimized cluster number and low transmission efficiency, which hinder its performance. This paper proposes an improved LEACH protocol for cluster-based UASNs, where the cluster number is optimized with an underwater energy propagation model to reduce energy consumption, and a transmission scheduling algorithm is also employed to achieve conflict-free parallel data transmission. Replication computing is introduced to the LEACH protocol to reduce the signaling in the clustering and data transmission phases. The simulation results show that the proposed protocol outperforms several conventional methods in terms of normalized average residual energy, average number of surviving nodes, average round when the first death node occurs, and the number of packets received by the base station.