Abstract: As the most widely-used method for motion control of quadruped robot, virtual mode control （VMC）can achieve compliant interaction between foot and ground at the cost of trajectory tracking precision. A fractional-order VMC (FOVMC) was proposed to improve the robustness and precision of VMC for single-leg tracking of hydraulic quadruped robot. And the implementation detail about the frequency domain modeling process of force control system for hydraulic-cylinder-driven joints and optimization-based FOVMC parameter tuning method were provided. Some trotting experiments were carried out on a quadruped robot platform to validate that the superiority of FOVMC over classical VMC in performance improvement of single-leg motion control.