Aim to the application of robot in the fields of engineering exploration, anti-terror, military spy and other related areas, one robot with the structure of wheeled foot and quadruped is researched, which combines the priorities of both wheeled robot and legged robot. The design principle of quadruped robot is introduced. The serial inverse kinematics of swing leg and Parallel inverse kinematics of supporting legs are analyzed independently. Based on zero moment point principle, walking gait and dynamic stability is planned. At the same time, such dynamic walking is optimized by simulation. At last moving ZMP strategy is adopted in walking experiment. The walking experiment shows that this strategy can effectively reduce the max value and changing range of robot body acceleration and realize dynamic stability and smoothly walking of robot.