Abstract: A new stepregression method for fitting ground motion data to obtain an attenuation relation is suggested in this paper. As an example, this method is applied to find attenuation relation for acceleration response spectra platform level of western U.S.,using strongmotion data supplied by PEER NGA project. Fitted result shows that the final prediction equation is unbiased and stable, and can well characterize the distancesaturation and magnitudesaturation in nearfield with large magnitude. It also shows that in the farfield the attenuation rate of ground motion is correctly predicated by accounting for data truncation.