For a quadruped robot to implement steady moving on horizontal planes, avoiding the impact against the ground, a foot trajectory planning method underling low contact impact was presented. At first, kinematic model of the quadruped robot though D-H algorithm have been established. Then, the foot trajectories, which are continuous not only in displacements and velocities but also in accelerations, was scheduled based on the walking gait. Lastly, the steering and straight line movements of the robot were simulated, simulation experiments show that the quadruped robot motion stably on horizontal planes without impact and sliding.