Abstract: Axisymmetric wave propagation and attenuation along viscoelastic cylindrical tube are investigated within the framework of Kelvin-Voigt linear viscoelastic model. Non-dimensional phase velocity and attenuation of axisymmetric viscoelastic wave propagation are obtained by a complex root searching program. The characteristics of axisymmetric waves propagation are compared between viscoelastic cylindrical tube and elastic cylindrical tube. The influences of porosity and loss factor and material parameters on phase velocity and attenuation are given. The results show that there exist attenuation in all propagation modes along viscoelastic cylindrical tube, and higher-order propagation modes haven't cut-off frequency. Loss factor has little influence on phase velocity of first mode and large influence on attenuation. Porosity has large influence on both phase velocity and attenuation.