It is suggested that the pulse-like ground motions, in the near-fault region, have great impact on the building seismic design. However, the theoretical study on the building response to the pulse-like ground motions input is not sufficiently clarified yet. In this study, the time at maximum response is theoretically evaluated as important factor. Based on that, the theoretical solutions of response spectra, with single-degree-of-freedom system subject to the sinusoidal pulse input, are performed. In addition, we suggested the damping-modification-factor, in accordance with the time at maximum response and the pulse wave period - building period relations.