This paper proposes a control algorithm for pace gait of a quadruped walking robot, using a passive dynamics autonomous control algorithm (PDAC). The PDAC realizes an efficient motion based on the intrinsic dynamics of a robot. This paper first calculates an energy consumption of the pace and a crawl gait at various walking parameters such as a stride length and a walking period. The optimal walking parameters are obtained for each gait at various walking speed in the simulation and their parameters are confirmed by applied to an experimental walking robot. The trend of the energy consumption transition measured in the experiments are similar to those in the simulation. For example the consumption energy of the pace gait becomes less than that of crawl gait when a walking speed becomes relatively high. As a result, quadruped walking parameters corresponding to the desired walking speed such as the type of gait, the stride length and the walking period are designed on the energy-consumption-basis.