Abstract: Based on the linear three-dimensional elastic theory and Kelvin-Voigt model, the wave equation of longitudinal guided waves in the viscoelastic anisotropic hollow cylinder was derived by using the Legendre polynomial expansion method, and the decoupled wave equation was solved numerically while the implications of the related equations were fully expounded. In order to validate our program, the dispersion curves and attenuation curves of the viscoelastic hollow cylinder with a large ratio of radius to thickness were calculated in comparison with the available date. Meanwhile, the displacement distribution and stress distribution were further calculated for the reliability of the method. Then, the influence of the ratio of radius to thickness and the effect of viscous constants were investigated respectively, which contains the dispersion curves and attenuation curves of longitudinal modes and torsional ones. The effects of viscoelastic parameters to the torsional waves were illustrated.