A proper walking pattern is to be assigned for a walk of multi-legged robots. For the purpose of identifying a good walking pattern for multi-legged robots, this paper consider a simple model of quadruped robotic walking and analyze its walking balance based on the centroid of foot polygons formed in every step. A performance index to estimate the walking balance is also proposed. Simulation studies show that the centroid trajectory of foot polygons and the walking balance in a common quadruped walking are different according to the walking pattern employed. Based on the walking balance index and a bio-mimetic aspect, a useful walking pattern for quadruped robots is finally addressed.