In this paper, the single leg hydraulic drive system of the quadruped robot is taken as the research object. Then the nonlinear mathematical model of the hydraulic system is built. According to the real mechanical structure parameters of the single leg, the relationship between position control characteristics of the system and variation of single leg trajectory is investigated. Besides, the tracing accuracy of single leg foot displacement in one trot gait condition is analyzed through combination of kinematics solution and simulation analysis. In conclusion, the research indicates that the nonlinear mathematical model can be used to analyze the position control performance of the single leg hydraulic drive system. This research provides a basic foundation for further research of control method.