The bionics of control and the stability of walking are two important aspects in the gait research of quadruped robots. In order to improve the stability of quadruped robot motion, this paper constructed a CPG model using a Hopf oscillator, which achieved various gaits and transitions between them. We compared the advantages and disadvantages of gait control methods based on CPG and gait planning methods based on trajectory planning in walking. In order to simultaneously utilize the advantages of CPG control and trajectory planning, a neural network is proposed to nonlinearly map the CPG control curve with the driving curve obtained from the inverse kinematics of the foot trajectory, so that the quadruped robot has biomimetic characteristics in control and zero impact characteristics in foot contact. The simulation and experimental results show that the theoretical walking speed of the quadruped robot using CPG gait generation method and trajectory planning method is similar to 80 mm/ s. However, the lateral displacement of the quadruped robot using CPG gait generation method is within ±10 mm and the pitch angle is between ±1. 5°, while the lateral displacement of the quadruped robot using trajectory planning control method is within ±35 mm and the pitch angle is between ±4°, It can be seen that the performance of the two control methods on lateral displacement and pitch motion is inconsistent. Through experimental measurements, it is known that the robot adopts a walk gait with a walking speed of 18. 57 mm/ s, which is close to the theoretical walking speed of 20 mm/ s. After gait conversion, it walks in a trot gait with a walking speed of 76. 15 mm/ s, which is close to the theoretical walking speed of 80 mm/ s. A small error may be caused by assembly and slipping during walking. By measuring its lateral displacement, it can be seen that the lateral displacement is within 15 mm on the left and 25 mm on the right, both of which are within an appropriate range, proving the effectiveness of the proposed algorithm.