A　second-order　asymptotic　analysis　method　is　developed　for　the　Steklov　eigenvalue　problem　in　periodically　perforated　domain.　By　the　two-scale　expansions　of　the　eigenfunctions　and　eigenvalues,　the　first-　and　second-order　cell　functions　defined　on　the　representative　cell　are　obtained　successively,　the　homogenized　elliptic　eigenvalue　problem　is　formulated,　and　effective　coefficients　are　derived.　The　first-　and　second-order　correctors　of　the　eigenvalues　are　expressed　in　terms　of　the　integrations　of　the　cell　functions　and　homogenized　eigenfunctions.　The　error　estimations　of　the　expansions　of　eigenvalues　are　established,　and　the　corresponding　finite　element　algorithm　is　proposed.　Numerical　examples　are　carried　out,　and　both　qualitative　and　quantitative　comparisons　with　the　solutions　by　classical　finite　element　computations　are　performed.　It　is　demonstrated　that　this　asymptotic　model　is　effective　to　capture　the　local　details　of　the　eigenfunctions　by　considering　the　second-order　expansion　terms,　and　the　algorithm　presented　in　this　work　is　efficient　to　obtain　the　accurate　spectral　properties　of　the　porous　material　at　lower　cost.