The principle of passive dynamic walking has drawn lots of attentions in the field of robotics for it provides a possibility to realize natural walking. However, stabilizing the quadrupedal passive walking remains challenging. In this paper, a novel control method is proposed to stabilize the quadrupedal quasi-passive walking. Inspired by biological concepts, this method treats the foreleg pair and hindleg pair as two bipedal walkers, and a virtual model controller is designed to maintain the quasi-passive walking of each bipedal walker independently. This control method was then verified by a planar quadrupedal model with compliant legs, which successfully achieved stable periodical walking gaits. It was found that although being controlled independently, the movement of fore and hind leg pairs still formed a time-invariant phase shift, showing remarkable resemblance to that of a walking horse. We further analyzed the influences of varying factors on the gait characteristics and stability. These analyses show the control method is robust since it can stabilize the gaits within a wide range of leg compliance parameters and resist considerably large disturbances. In addition, the optimal ranges of the leg compliance parameters for the largest stability margin were also found in this study.