Quadruped robot is widely developed on the basis of bionic technology and has good structural stability and flexibility in uneven terrain. It is required of the quadruped robot to keep static balance while transportation task is executed. In this paper, first, the unstable problems during static walking on a slope have been analyzed in detail, and the stability criterion which considering affections of slope walking environment has been proposed. Based on static balance, the falling over problem and tumbling around the line connecting two support feet during gait transition problem have been solved. The gaits are planned to ensure omni-directional stable walking on a slope. Through walking experiments by computer simulation, the validity of the proposed method has been verified.