Abstract: For the problem of trajectory tracking between joints of a snake-like robot in flow field, a trajectory tracking control law based on an improved serpentine curve for snake-like robot to avoid obstacles in flow field is studied. Firstly, considering the external disturbance that the fluid environment may impose on the snake-like robot system, the fluid-structure interaction model of the obstacle passage and the snake-like robot is established in the flow field by using the immersed boundary-lattice Boltzmann method (IB-LBM). Then, a potential function is added to the snake-like robot to avoid obstacles, and an improved serpentine curve equation is used to track the head trajectory for the tail joints. Finally, the effects of different flow field densities, tail swing frequencies of robot and Reynolds numbers on trajectory tracking of the snake-like robot are studied by Matlab simulation and experiment. Theoretical analysis and numerical simulation show that the designed trajectory tracking control law can not only make the snake-like robot track the trajectory of the previous joint when it encounters obstacles, but also stabilize the transverse distance, longitudinal distance and direction angle to achieve the purpose of effectively avoiding obstacles. Moreover, the joints of the snake-like robot will recover the serpentine curve motion after avoiding obstacles, to provide continuous power for the snake-like robot. The simulation and experimental results verify the effectiveness of the trajectory tracking control law.