Abstract: Aimed to improve the walking ability of a quadruped robot on uneven terrain, the stable condition in marching process was analyzed based on zero moment point (ZMP) theory. By employing the concept of stability margin, the optimal stability point (OSP) was calculated for ZMP planning. To reduce energy consumption and speed loss from wagging the body frequently, a novel scheme of calculating OSP in the suboptimal supporting triangle (SST) was proposed. Body posture and supporting points were designed to achieve trade-off between legs' work space and robot's stability. And the zero impact algorithm was improved to adapt the given supporting points and angles of slope and body. Simulations showed that the prototype robot is able to walk steadily on different slopes controlled by the given planning method.