Abstract This study aims to quantify the acceleration and displacement response spectra of pulse-like near-fault ground motions, which can be further employed to derive the seismic force demands of a structure system or structural member. The spectra are computed based on a set of pulse type ground motions, and the spectral shapes are derived by normalizing the spectra with the spectral values at the pulse periods. The normalized spectral values exhibit very small variations at periods larger than the pulse period but very large dispersions at periods shorter than the pulse periods. In a bi-normalization coordinate, an empirical function is developed for simulating the normalized spectral shape, in which the damping effect is included. Moreover, another empirical function for estimating the spectral value at the pulse period is constructed. The two-step procedure finally leads to a function for estimating acceleration spectral values based on the structural period, structural damping and pulse period of ground motion. The displacement spectra of high damping systems are further developed by employing the damping modification factors for acceleration and displacement spectra. On average, the spectra estimated by the proposed model are in agreement with the true spectra. Combined with the prediction of key parameters of ground motions in near-fault zones, the proposed record-based spectral model is expected to produce a design spectrum better than code-based design spectra.