Abstract: After discussing the seismic mitigation effect of soil stiffness，scarp height，and number of spans under the scarp on viscoelastic frame structure with special-shaped cloumns connected with ground by multiple-floor，the conclusions were as follows: 1) The natural vibration frequency of structure decreased with the soil stiffness decrease， increased with the scarp height increase，and decreased with the spans under the scarp increase． But when the scarp height increases to a certain extent，the higher order frequency would be reduced． 2) The soil stiffness effect on structure was related to the inputting of seismic motion． When the inputting wave contained less high frequency，the seismic responses might increase with the soil stiffness decrease． When the inputting wave cantained more high frequency，the seismic responses might be reduced on softer soil ground． 3) The effect of scarp height and number of spans under the scarp on uncontrolled structure was related to the inputting of seismic motion，while on controlled structure it had less relation to the inputting of seismic motion． And the responses of floors under the scarp had greater impact than floors above when the scarp height and number of spans under the scarp were changed． 4) The ground and inputting wave would both affect the control efficiency of viscoelastic structure on scarp． The ground condition and earthquake group of the site must be both taken account seriously when designing the damping device．