This paper presents a target tracking control method for a biomimetic underwater vehicle named RobCutt-II. The RobCutt-II is propelled by double undulatory fins which are distributed on both sides. In order to implement target tracking and observation in a certain distance, we propose a method by decoupling the target tracking control problem into distance, heading and depth control problems. Based on this idea, we design a target tracking controller composed of a navigation system, a distance controller, a heading controller, a depth controller and a switching logic controller. The simulation results verify the effectiveness of the proposed method on the biomimetic underwater vehicle.