Currently, underwater sensor networks are extensively applied for environmental monitoring, disaster prediction, etc. Nevertheless, owing to the complicacy of the underwater environment, the limited energy of underwater sensor nodes, and the high latency of hydroacoustic channels, the energy-efficient operation of underwater sensor networks has become an important challenge. In this paper, a high-efficiency clustering routing protocol in AUV-assisted underwater sensor networks (HECRA) is proposed to address the energy limitations and low data transmission reliability in underwater sensor networks. The protocol optimizes the cluster head selection strategy of the traditional low-energy adaptive clustering hierarchy (LEACH) protocol by introducing the residual energy and node degree in the cluster head selection phase and performs some optimizations in the cluster formation and data transmission phases, including selecting clusters for joining by ordinary nodes based on the residual energy of the cluster head nodes and weight computation based on the depth and residual energy of the cluster head nodes to select the optimal message forwarding nodes. In addition, this paper introduces an autonomous underwater vehicle (AUV) as a dynamic relay node to improve network transmission efficiency. According to the simulation results, compared with the existing LEACH, the energy efficient routing protocol based on layers and unequal clusters in underwater wireless sensor networks (EERBLC) and energy-efficient clustering multi-hop routing protocol in a UWSN (EECMR), the HECRA significantly improves network lifetime, the residual node energy, and the number of successfully transmitted packets, which can effectively prolong network lifetime and ensure efficient data transmission.