To study the effect of three limit states (force limit state, displacement limit state, and compound limit state) of a liquid viscous damper on the seismic response of single-degree-of-freedom (SDOF) systems, the three limit states of the viscous damper were simulated, and a reliable numerical analysis model was obtained by Ruaumoko-2D. Then, the reinforced concrete structures of two and ten storeys were modelled into two equivalent SDOF systems, each of which was connected in parallel with a viscous damper. Time history analyses under the increasing action of multiple seismic waves and sine waves were conducted respectively to investigate the influence of the force limit state, displacement limit state, and compound limit state of the viscous damper on the SDOF system response. By comparing with the SDOF systems without considering limit states, the variation of the displacement ratio with the peak speed of the ground motion was obtained.