Hydraulic quadruped robots can adapt to very complex ground conditions, as they have good maneuverability and high load capacity and, therefore, have received great attention in military research fields all over the world. However, there is no mature theory on how to ensure stable, efficient and fast walking of robots. In this paper, from the point of view of the natural frequency of the hydraulic system, we first calculate the natural frequency of the robot's legs during the whole motion period of the robot, and verify the accuracy of calculation through system identification. Then through the analysis of the state equation and transfer function matrix of the MIMO system, it is found that the zero and pole of the system are very close, this is why the natural frequency is low but the system response is acceptable and then we prove that no parameter for the simultaneous zero-pole cancellation of two hydraulic cylinders exists. With the goal of increasing the natural frequency, we optimized the leg structure of the robot to find the best structural parameters. Finally, a single-leg test bench was built. The experimental results show that the optimization of the structure can actually increase the natural frequency of the system and significantly improve the response characteristics of the robot.