It is essential to determine a proper earthquake time history as a seismic load in a seismic design for a critical structure. In the code, a seismic load should satisfy a design response spectrum and include the characteristic of a target fault. The characteristic of a fault can be represented by a definition of a type of possible earthquake time history shape that occurred in a target fault. In this paper, the pseudo-basis function is proposed to be used to construct a specific type of earthquake, including the characteristic of a target fault. The pseudo-basis function is derived from analyzing the earthquake time history of specific fault harmonic wavelet transform. To show the feasibility of this method, the proposed method was applied to the faults causing the Gyeong-Ju ML5.8 and Pohang ML5.3 earthquakes.