In this paper, the dynamic behaviors of a multi-span viscoelastic functionally graded material pipe conveying fluid are investigated by dynamic stiffness method. The material properties of the functionally graded material pipe are considered as graded distribution along the thickness direction according to a power-law. Several numerical examples are performed to study the effects of volume fraction exponent, fluid velocity, internal pressure, and internal damping on the stability and frequency response of the fluid-conveying functionally graded material pipe. It’s found that the viscoelastic functionally graded material pipe exhibits some special dynamic behaviors and it could increase the stability significantly when compared with the aluminum and steel pipes. The numerical results also demonstrate that by the introduction of the functionally graded material, the stiffness of the piping system could be modulated easily by designing the volume fraction function. Therefore, if the dominant frequency contents of the external loads are known, a preferable design of the functionally graded material pipe to reduce the vibration is possible.