The　Laplace　transform　method　is　widely　used　for　solving　viscoelastic　dynamic　problems.　However,　the　numerical　inversion　process　of　this　method　suffers　from　instability,　especially　for　long-duration　response　issues.　Moreover,　the　solutions　obtained　via　the　Laplace　transform　method　are　often　semi-analytical.　In　this　study,　addressing　the　one-dimensional　transient　response　problem　of　unsaturated　viscoelastic　porous　media,　an　analytical　solution　is　proposed　based　on　the　finite　Fourier　transform　method.　First,　leveraging　the　symmetry　of　the　problem,　the　solution　of　a　typical　stress-displacement　boundary　problem　is　transformed　into　the　solution　of　a　stress-stress　boundary　problem.　Second,　by　applying　finite　Fourier　sine　and　cosine　transforms,　the　original　second-order　viscoelastic　partial　differential　governing　equations　are　transformed　into　a　system　of　first-order　ordinary　differential　equations　in　the　frequency　domain　for　solution,　and　the　analytical　solution　in　the　frequency　domain　is　provided　using　the　state-space　method.　Finally,　the　finite　Fourier　inverse　transform　method　is　used　to　present　the　analytical　solution　in　series　form　for　the　original　problem　in　the　time　domain.　The　accuracy　of　the　proposed　method　is　validated　through　comparison　with　the　Laplace　solution　method　and　existing　elastic　solution　results.　The　analysis　of　numerical　examples　shows　that　the　damping　coefficient　has　a　significant　influence　on　the　wave　velocity.　As　the　damping　coefficient　increases,　the　wave　phase　generally　tends　to　decrease.　With　the　increase　in　saturation　,　the　velocities　of　and　waves　increase,　while　the　velocity　of　the　wave　decreases.