Empirical regional attenuation relationships for the amplitude of S and Lg waves were achieved by performing regressions over a large number of accelerograms, collected from TSMIP stations in southwestern Taiwan over a ~7-year period. From estimations of effective ground-motion duration, utilized to characterize the source term and path effects, a piecewise continuous duration function relating to hypocentral distance was derived. For simplicity, Brune’s ω-square model was used in this article. Assuming a high-frequency approximated decay parameter of κ0= 0.03 sec and static stress drop Δσ= 100 bars for the averaging characteristics of the source spectra, the attenuation curves of peak horizontal accelerations that relate to the hypocentral distance for the given moment magnitudes were effectively obtained using random vibration theory. However, the current model cannot be arbitrarily generalized for the prediction by individual specific earthquake and does not include extended faults based on the source assumption applied. Due to sensitive variation of peak ground motion predictions (strongly associated with the stress drop and attenuation factors), it is suggested that the source parameters and the sites chosen should be localized into several subsets (as far as this is possible) through analyses of historic earthquakes and strong-motion records. In practice, this work should be valid in predicting peak ground motions well when simulating a characterized event.