The non-stationarities of ground motion may significantly affect the results of site response analysis. To approximately and quantitatively control the groundmotion characteristics of input bedrock-acceleration, a ground-motion simulation method representing the target non-stationarities is firstly established based on the time-frequency modulating function. Then, three bedrock-motion records with different predominant-frequency characteristics are selected, and two forms of modulating function are introduced for simulating temporal and spectral non-stationarities, respectively. Based on those, three input bedrock-motion scenarios with different time-frequency characteristics are designed for site response analysis, 42 artificial ground-motions are simulated. Finally, nonlinear site response analysis is performed on three types of sites to investigate the effects of spectral non-stationarity of bedrock motion on the surface peak ground acceleration (PGA_surf) and spectral acceleration (SA_surf). The results show: ①The proposed ground-motion simulation method based on the time-frequency modulating function is competent for simulating ground motion with well-controlled temporal and spectral non-stationarities simultaneously. ②For bedrock motion with significantly time-varying frequencies, ignoring spectral non-stationarities in ground-motion simulation may underestimate the hazard on ground surface. The harder thesoil, the higher PGArock is, and the more remarkable the underestimation shall be. ③The influence of time-varying frequency on the high-frequency parts of SAsurf correlates with the concentrated time of high-frequency contents and characteristics of site: if the high-frequency contents of bedrock motion concentrates at the strong-motion phase, SAsurf obtained from the temporal-nonstationary-only artificial motions shall be more conservative for on relatively hard site. ④The influence of time-varying frequency on surface/bedrock response spectral ratio (RSR) correlates with the site classification and natural vibration frequency (f) of structure. If PGArock is high, the influence is more distinct at about 5Hz for relatively hard site; while, on relatively soft sites of classification III or IV, the influence is more distinct at about 1Hz. Therefore, when simulating bedrock motions, especially those with high peak values, one shall use fullynonstationary method in combination with the factors such as natural vibration frequency of structure, site condition, and requirement of specific project, to consider the spectral nonstationary characteristics. The research results proposed here are constructive for setting reasonable parameters to simulate bedrock motion.