For　large　linear　non-classically　damped　system,　when　mode　superposition　method　based　on　complex　vector　is　used　to　analyze　seismic　responses,　the　amount　of　calculating　total　mode　vectors　using　Jacobi　method　is　fairly　large　and　unpractical　indeed.　In　this　paper,　Lanczos　algorithm　and　subspace　iteration　method,　which　are　effective　in　computing　modes　of　classical　damped　linear　system,　are　extended　and　modified　to　find　a　set　of　real　vector　basis　to　reduce　freedom　of　primary　equation.　Combined　with　Foss　transform,　a　set　of　applied　complex　vector　basis　is　derived　to　analyze　the　first　order　complex　eigenpairs　for　dynamic　analysis　of　large　non-classically　damped　linear　system　under　random　excitation.　From　the　theoretical　analysis　and　numerical　examination,　it　could　be　pointed　out　that　the　complex　vector　basis　derived　in　this　paper　not　only　has　clear　physical　significance　and　good　computational　efficiency,　but　also　is　adapted　to　analyze　dynamic　responses　of　large　non-classically　damped　linear　system,　including　seismic　responses　in　time　domain　and　mode　superposition　based　on　seismic　design　spectra　in　frequency　domain.