An essential consideration when analyzing the gait of walking robots is their ability to maintain stability during walking. Therefore, this study proposes a vertical waist-jointed walking robot and gait algorithm to increase the gait stability margin while walking on the slope. First, the energy stability margin is compared according to the posture of the walking motion on slope. Next, a vertical waist-jointed walking robot is modeled to analyze the stability margin in given assumption. We describe new parameters, joint angle and position of a vertical waist-joint to get COG (center of gravity of a body) in walking. Finally, we prove the superiority of the proposed gait algorithm using simulation and conclude the results.