Complex hydrodynamic modeling and analysis are considered as stumbling blocks in the motion study of underwater bionic robots. In recent years, reinforcement learning techniques have been applied for robot motion control in unknown environments. However, robots may act in an unconventional or dangerous manner during the learning process. These actions increase the training difficulty and decrease the training efficiency. In this study, a biological-inspired reinforcement learning control method is proposed. It realizes the self-learning movement policy of the robot with discretized swimming motions of a beaver without the need to establish motion models, such as hydrodynamics, of underwater robots. The biological-inspired model further reduces the robot’s ineffective movements during the reinforcement learning and improves training efficiency. The experiment results verify the environmental adaptation and self-learning ability of the proposed robot platform and proves the effectiveness of the reinforcement learning control method for robotic swimming based on biological inspiration. This study’s findings provide new ideas for the motion control of underwater bionic robots and further promote the application of artificial intelligence in underwater robots.