There are many types of walking robots in the world. For dynamic walking of the robots it is necessary to keep its dynamic stability. The dynamic stability is influenced by the position of ZMP (zero moment point). In this paper we study the control of the ZMP position of walking robot. For experiment we developed a quadruped robot and analyzed the dynamic stability of the robot. Developed robot has 2 joints at each leg and WBO (weight balancing oscillator) on the body of the robot. The WBO is designed to move linearly from side to side when the robot walks dynamically. Walking test was performed to verify the validity of the proposed methods. Especially we showed that the dynamic stability of the robot can be improved without sacrifice of the walking speed by control the WBO.