A longitudinal vibration coupling with a flexural vibration in a curved fluid-filled periodic pipe is studied. The pipe is fabricated by a periodic composite material structure based on the Bragg scattering mechanism of Phononic Crystals. Using the transfer matrix method, the band structure of an infinite periodic straight pipe is calculated, and the elastic wave propagation characteristics of the periodic pipe are discussed. Furthermore, the vibrational frequency response functions of a finite curved pipe are performed and the coupled vibration is studied. Finally, the transmission properties of longitudinal vibration, flexural vibration and their coupling vibration in the curved periodic fluid-filled pipe are investigated.