In order to understand fully the effect of strong ground motion containing velocity pulse on constant-ductility long-period inelastic spectra, we synthesize two time histories, not containing velocity pulse, whose elastic spectra are identical to that of original time history containing velocity pulse, and whose peak accelerations are as big as that of the original time history. The reason why we synthesize two time histories for one original time history is to avoid the effect of randomicity in selecting sample. We select two time histories of 1999 CHi-CHi earthquake as original time histories, one of which has two synthesized counterparts. It is found that although the elastic response spectra of original time histories are identical with those of their synthesized counterparts, their constant-ductility long-period inelastic spectra are different. We consider that the difference results from the velocity pulses which exist in the original time histories.