In view of an improvement of the stability of the quadruped robot trot gait, thus alleviating the problem two swinging legs’ failure at landing at the same time, a gait planning has been carried out from the following two aspects: optimization of the trajectory function of the extremities and selection of the initial position of the extremities. The kinematics model of quadruped robot is to be established by D-H method, with the inverse kinematics solution obtained by adopting geometric method. The trajectory function of the extremities is optimized based on the zero impact principle, with 8 different extremities positions selected for simulation, followed by an analysis of the motion stability of the quadruped robot from aspects of foot impact force, body displacement, pitch angle, roll angle and yaw angle. The comparative simulation results show that the trot gait motion of the quadruped robot is more stable by using the optimized extremities trajectory and the optimized extremities position.