Using a double-layer horizontal strata model, a simplified time-history analytical method which considers liquefiable layer existence is proposed for calculating ground motion acceleration and displacement. Solutions in frequency and time domains under arbitrary loading are given. By the cycle-by-cycle method, the calculating results of ground acceleration and displacement time histories under arbitrary loading are presented. Adopting a proper pore-water pressure ratio incremental model, shear modulus of the liquefiable layer is modified cycle by cycle that the nonlinearity of the liquefiable layer induced by soil liquefying is proximately simulated. Through numerical analysis, ground displacement on liquefied sites is much larger than that on non-liquefied sites during liquefaction process. Before initial liquefaction, ground displacement and acceleration on liquefied sites are obviously higher than those on non-liquefied sites. After initial liquefaction, ground acceleration remarkably decreased but displacement remains much larger than that on non-liquefied sites. Normalized acceleration response spectra are calculated. It shows that the low period components on liquefied sites are lower than those on non-liquefied sites, but long period components are higher than those on non-liquefied sites.