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.　©　2019,　Editorial　Office　of　Acta　Materiae　Compositae　Sinica.　All　right　reserved.