Recently, underwater wireless communication (UWC) networks have garnered significant attention. In specific application scenarios, underwater electrocommunication technology exhibits distinct advantages over traditional acoustic and optical communication methods, emerging as a viable alternative for communication among autonomous underwater vehicles (AUVs). Most AUVs depend heavily on battery power, where the energy is highly precious. Given that the reliability of AUVs communications is tethered to limited energy storage, the imperative for energy-efficient communication strategies is paramount. The issue of power consumption control in underwater electrocommunication systems is addressed in this research by proposing an adaptive power control strategy based on transfer learning for transferring power. The method can predict the minimum voltage across the transmitting electrodes required to satisfy the communication task according to the changes in the operating environment and adjust the transmitting power level accordingly. To verify the effectiveness of this method, this paper establishes a transfer network based on simulation data obtained by finite element simulation combined with the theory and technique of transfer learning. It uses experimental samples to verify the effectiveness of this network in shallow waters. According to the findings, the transfer network outperforms the ordinary backpropagation neural network trained solely on experimental samples in terms of performance.