In most applications of the stochastic Green’s function simulation, amplitude characteristics of seismic responses at target sites are taken into consideration, but phase information of them is often disregarded or just assumed to be random. However, when seismic waves from the source pass through different geological strata, they take multiple paths and, as result, the arrival times of different seismic phases to the receiver vary. Especially in basin structures, seismic waves trapped in unconsolidated deposits or secondarily induced at the basin edges elongate the duration of ground motion. In the present study, a simple empirical method using the Meyer–Yamada wavelet procedure is proposed for the phase-dependent site response estimation in time domain. The method reveals the amplitude and phase effects of extended duration of ground motion on site response by utilizing the wavelet transform. Because the wavelet transform yields a localization of a signal in both frequency and time domains, the phase information of the signal stays intact. Application of this method has been performed using the aftershock records of the 1999 Düzce, Turkey Earthquake (Mw 7.1). Amplitude spectra of absolute site responses were also calculated by a spectral calculation method at each station for comparison purpose. Good agreement between the amplitude spectra calculated with the wavelet method and those of the spectral calculation method supports the efficiency of the proposed method.