An acceleration wavelet function, which is located in a time interval with finite length and does not have the problem of baseline drift, is constructed in this study. Utilizing the constructed wavelet as a corrective function, an iterative spectral matching method is proposed. The method superimposes the corrective wavelets onto any given initial ground‐motion acceleration to modify it to match the target response spectra with the required precision. This method not only avoids any additional baseline drift by virtue of the method of construction used for the corrective wavelet, but also can preserve the general nonstationary characteristics of the initial ground motion because of the localized nature of the corrective wavelet. Numerical examples demonstrate the capability of the proposed method in matching the target multidamping response spectra, especially in retaining the basic features of the original seed ground motions.