Koi carp is used as a bionic object to study the swinging propulsion characteristics of its torso and tail fin. According to the morphological characteristics of the fish, the geometric model of the bionic fish is established. Different kinematic models are established according to the swing posture of the torso and caudal fin. Then, using the dynamic grid technology and writing the UDF program to control the fish body, the movement state of the bionic fish driven by the two governing equations was simulated numerically. The effects of different motion frequency, swing amplitude and incoming flow velocity on swimming speed, acceleration, displacement and pressure distribution of bionic fish are studied, and the propulsive performance characteristics of bionic fish swing under two governing equations are revealed. The results show that, driven by the two governing equations, no matter how the movement frequency changes, the biomimetic fish reaches the steady state at the same time, and the swimming distance in the same period is similar. When the oscillation amplitude was 30°, the bionic fish reached the steady state in the shortest time, and the fluctuation was relatively small, which was the best amplitude. When the incoming flow velocity is lower than 0.1, it can swim stably in the flow field. In the stable swimming state, the high pressure and low pressure are distributed at both ends of the caudal fin to push the fish forward, which is consistent with the reality.