In this paper, we propose an adaptive gait by which a quadruped walking robot can walk against external disturbances. This adaptive gait mechanism makes it possible for a quadruped walking robot to change its gait and accommodate external disturbances form various external environmental factors. Under the assumption that external disturbances can be converted to an external force acting on the body of a quadruped walking robot, we propose a new criterion for the stability margin of a waling robot by using an effective mass center based on the zero moment point under unknown external force. And for a solution of an adaptive gait against external disturbances, an method of altitude control and reflexive direction control is suggested. An algorithmic search method for an optimal stride of the quadruped mehtod, the gait stability margin of a quadruped walking robot is optimized in changing its direction at any instance for and after the reflexive direction control. To verify the efficiency of the proposed approach, some simulaton results are provided.