To enhance the joint control performance in hydraulic quadruped robots, active disturbance rejection control was used in the leg joint controller design of a hydraulic quadruped robot in combination with the self-growing lévy-flight salp swarm algorithm in this paper. First, the robot-leg structure of the hydraulic system model was built to analyze system operation details in terms of the mathematical construction. Second, the self-growing lévy-flight salp swarm algorithm was introduced. Then, the active disturbance rejection control parameters required were defined based on the composition and principle of the third-order active disturbance rejection control model. Third, the system evaluation function ITSE was selected, and the parameter tuning problem was converted into an algorithm optimization problem. Finally, the joint system of the hydraulic quadruped robot was taken as the research object, the self-growing lévy-flight salp swarm algorithm was added to the active disturbance rejection control to tune parameters, and this paper compared three different algorithms in the same environments to show the good control ability of the proposed method. To comprehensively show the performances of robot joint systems controlled by the proposed controller, the temporal response results, the frequency response results, the sawtooth response results, the ramp response, and the random response were displayed. All results reveal the effectiveness and excellent performance of the proposed controller in joint systems of a hydraulic quadruped robot.