Based　on　the　complex　modal　superposition　theory,　the　original　error　of　complex　mode　truncation,　which　is　used　to　analyze　the　non-classically　damped　linear　system,　is　studied　and　the　error　formula　is　obtained.　Similar　to　higher　modal　responses　of　classical　damping　systems,　the　form　of　response　ratio　shows　that　with　the　decrease　of　the　ratio　of　input　frequency　and　natural　frequency　the　displacements　of　higher　complex　modal　equations　can　also　represented　by　static　displacement　of　dynamic　load.　Therefore,　because　of　this　fact,　static　correction　method　and　modal　acceleration　approach　about　non-classical　damping　systems　are　derived,　whose　forms　are　the　same　as　that　of　the　conventional　methods.　In　addition,　the　correction　methods　of　both　real　and　complex　modal　superposition　approaches　are　unified　according　to　the　condition　of　complex　modes　degenerating　to　real　modes　(real　part　is　proportional　to　imaginary　part).　At　last,　the　effectiveness　of　correction　methods　is　verified　through　a　numerical　example,　particularly　for　the　case　that　the　major　natural　frequencies　are　beyond　the　input　significant　frequency　range;　in　addition,　it　is　observed　that　rising　the　added　damping　will　reduce,　to　some　degree,　the　efficiency　of　the　modified　method　since　the　added　damping　decreases　some　high-order　natural　frequencies.　©　2017,　Nanjing　Univ.　of　Aeronautics　an　Astronautics.　All　right　reserved.