In order to improve the stability of diagonal trot gait for quadruped robot, a foot end trajectory planning method based on Bezier curve is proposed. Aiming at the diagonal trot gait of quadruped robot, the kinematics model of parallel legs of quadruped robot is established, the forward and inverse kinematics are solved by geometric method, and the foot end trajectories of swing phase and support phase are optimized based on zero impact principle and PD controller. The comparative test is carried out by using Webots simulation platform and experimental prototype. The results show that when the proportional coefficient in X direction is 20, the differential coefficient is 0.75 s, the proportional coefficient in Y direction is 20 and the differential coefficient is 0.5 s, the foot end trajectory of quadruped robot is smooth without sudden change of speed and acceleration, and the gait of diagonal trot is more stable.