This paper presents a bio-inspired mechanism design for a quadruped walking robot. The approach is derived from the observation on the behaviors of quadruped locomotion, skeletal structure, and the study on the stability of walking based on morphological analysis. In the first, we define the design parameters such as the dimensions of the body and limbs, the center of mass position, and locomotion mechanisms based on surveys on the literatures from biologists. Then, by using the parameters, we propose an useful framework for determining the design parameters of a quadruped walking robot. For implementations, we manufacture a dog-type self-contained quadruped walking robot, named AiDIN-III (Artificial DIgitigrade for Natural Environment version III) and the effectiveness of the proposed idea is validated via experimental works.