Underwater bionic robots have distinct advantages such as the high efficiency, high mobility and low noise etc. In this paper, a deep reinforcement learning based method is studied to control the robotic eel. Firstly, based on the propulsion principle of active and passive bionic mechanism, a robotic eel with two active rigid bodies and two compliant bodies is designed. Secondly, the robotic eel is modeled and simulated. The data collecting and training tasks are carried out in the simulation environment using deep reinforcement learning algorithms. The neural network with better performance is selected as the control function for the robotic eel. Finally, feasibility of the design and effectiveness of the control function are verified by a prototype via real experiments.