The composition characteristics and working principle of the hydraulic rotary system of the azimuth thruster were analyzed. The mathematical model of the rotary dynamic system of the pump-controlled hydraulic motor driving the gear reduction mechanism was established. Additionally, a fast tracking method for the azimuth angle of the azimuth thruster was proposed to analyze the rotary azimuth angle, angular velocity and dynamic response characteristics of the hydraulic system for different desired azimuth angles. The simulation results show that the established dynamic model can simulate the rotary motion response process of the real thruster, and can realize the rapid and accurate tracking of the azimuth angle. At the same time, the physical constraints of the rotary dynamic response were established. It provides an important reference for research on the motion control methods of dynamic positioning vessels.