Pilotis structures consisting of upper concrete bearing-walls and a soft first story have been well used in residential and office buildings in urban areas to primarily accommodate parking lots. In this research, drift-hardening concrete (DHC) columns developed by the authors are proposed to form the pilotis story with the aims of reducing its excessive residual drift caused by stronger earthquakes than anticipated in current seismic codes, mitigating damage degree, and enhancing resilience of the pilotis story. Nonlinear dynamic analysis was conducted to investigate the dynamic response characteristics of the wall structures supported by DHC columns. To this end, two sample six-story one-bay pilotis structures were designed following the current Japanese seismic design codes and analyzed. One sample structure is supported by ductile concrete (DC) columns, while the other is supported by DHC columns, which have the same dimensions, steel amount, and concrete strength as DC columns. Three representative ground motions were adopted for the nonlinear dynamic analysis. The analytical parameter was the amplitude of peak ground acceleration (PGA), scaled by the peak ground velocity (PGV) ranging between 12.5 cm/s and 100 cm/s with an interval of 12.5 cm/s. The analytical results have revealed that the residual drift of the pilotis story composed of DHC columns could be reduced to nearly zero under selected earthquakes scaled up to PGV = 100 cm/s, owing to not only the inherent self-centering ability of DHC columns but also the shake-down effect, which implies that the use of DHC columns can greatly enhance resilience of pilotis structures under strong earthquake inputs and promote its application in the buildings located in strong earthquake-prone regions. The maximum inter-story shear forces (MISFs) along the building height of the two models are also compared.