In view of realizing a stable walking of quadruped robots, it is necessary to lay out a reasonable plan of its foot trajectory. Based on Bezier curves, the foot end trajectory of quadruped robots has thus been planned, with the foot end trajectory optimized according to the constraint conditions of the foot end trajectory. On the basis of multiple groups of comparative experiments, the optimal coordinates of a group of control points can be determined, followed by a design of the foot end trajectory of the quadruped robot, thus obtaining the optimal combination of step length and leg lifting height. A simulation platform is built based on Matlab/Simulink for simulation experiments, followed by an analysis of the stability of the quadruped robots by comparing it with the impact force of foot end trajectory on foot end landing by using compound cycloid planning, the fluctuation range of the centroid, the yaw distance and the forward distance of the body. The simulation results show that the trajectory of the foot end planned by Bezier curves improves the stability of the robot motion.