This paper addresses a position control method of an underwater biomimetic vehicle-manipulator system (UBVMS) through reinforcement learning. The system description of the UBVMS with undulating fins is given. Considering the force/torqu generated by undulating fins and hydrodynamic force/torqu, the dynamic model of this UBVMS is established. The position control problem is modeled into a continuous-state, continuous-action Markov decision process (MDP) with a deterministic state transition algorithm based on the dynamic model. To solve this MDP, a reinforcement learning method is presented, which is based on the deep deterministic policy gradient (DDPG) theorem. The simulations of the position control in 5 cases are shown in the end.