This paper presents a novel deep reinforcement learning (DRL) method to solve the locomotion control problem of the biomimetic underwater vehicle (BUV) with hybrid propulsion, in order to meet the challenge of intractable multi-fins coordination and the complex hydrodynamic model. The system overview of the BUV, named RoboDact, with two flexible long fins and a double-joint fishtail as hybrid propulsion, is introduced. After that, the locomotion control problem is modeled as a Markov decision process (MDP) to be solved. Therefore, the locomotion control method based on soft actor-critic (SAC, a novel DRL algorithm) is proposed. The simulation environment is established based on the kinetic model for interaction. Finally, the feasibility and effectiveness of the proposed control method is demonstrated after extensive simulations. It will provide rich insights into the coordination control of biomimetic underwater vehicles.