In order to reduce the impact of the quadruped robot on the ground during walking, a fifth-order polynomial foot trajectory plan was proposed to improve the dynamic and static gait. The mathematical formula of the improved fifth-degree polynomial was deduced, and the inverse kinematics solution of the robot was calculated using the knowledge of robot kinematics. According to mathematical derivation, the theoretical curves of the speed and acceleration of the robot foot were analyzed. Using ADAMS to simulate the movement of the robot in the triangular and diagonal gait, the theoretical results of the foot trajectory and the simulation results were compared, and the change of the robot’s mass center and the change of the RPY angle in the simulation were analyzed. The theoretical analysis and simulation results are consistent, verifying the correctness of the improved foot trajectory.