Fluid and structure interaction induced vibration in pipe system conveying fluid occurs in many fields, and the flexural vibration control is very important. The idea of phononic crystals is introduced into the design of pipe system conveying fluid. Basing on Timoshenko beam equation, and using the transfer matrix method, we study the band gap properties of the vibration and its transmission properties. The effect of the material damping ratio and spring support stiffness on the band gap is analyzed. The existence of band gaps in the periodic pipe system conveying fluid lends new insight into vibration control of pipes.