This paper describes the development of a compact pneumatic valve that can obtain a high flow rate in a periodically pneumatically driven pipe-moving robot. Plumbing facilities around the world have fallen into disrepair in recent years. Pneumatically driven mobile robots are widely used as an inspection method due to the small inner diameter and complicated shape of the pipes. Various types of robots have been studied, such as earthworm, inchworm, and spiral tube robots. However, these robots are driven by existing pneumatic valve technologies, such as needle-type and solenoid valves, which limit the use of small mobile robots. Small pneumatic valves have a low flow rate, and the entire system is complicated because multiple air pressures are controlled by multiple electrical systems. Thus, focusing on the structure and periodic motion of the ball valve, we developed a pneumatic valve that can periodically apply pressure to multiple pneumatic actuators using only rotational motion with one degree of freedom. We also applied this pneumatic valve to a wave propagation robot and discussed the theoretical running speed of the robot with this valve.