Abstract: This paper presents a wavelet-based approach for estimating the root-mean-square (RMS) response of a linear single-degree-of-freedom (SDOF) system under earthquake ground motions. The time-frequency characteristics of the ground motion are analyzed using the wavelet method. The instantaneous power spectral density function (PSDF) of the response has been derived and used to estimate the instantaneous RMS response of the system. Numerical study of a single-degree-of-freedom (SDOF) system is performed. The result shows that the wavelet method can estimate the structural instantaneous RMS responses accurately.