Abstract: A new method of calculating earthquake response based on the cosine transform is proposed in order to improve the calculating accuracy of earthquake response spectra. Convolution and differential theorems of cosine transform are put forward and proved. By employing the transform as well as considering SDOF system’s dynamic differential equations as a starting point, the formula of cosine-transform-spectrum of earthquake responses is deduced, and then a general expression of response spectrum is obtained. For approaching the calculating accuracy, the response spectra of harmonic conditions is calculated by using exact and cosine transforms respectively. Meanwhile the error analysis is done. It is concluded that the mean square deviation of displacement, velocity and accelerate response spectra are 0.0012m, 0.003m/s and 0.16m/s2 respectively calculated by exact, while the result of cosine transform fit very well with theory, and the mean square deviation are 0.0002m, 0.002m/s and 0.36m/s2, when the load input is cos4πt, which shows the accuracy of displacement and velocity increased nearly 6 and 1.5 fold, although the mean square deviation of acceleration response spectrum is a little greater than that of an exact one; for the long period, the method of cosine transorm is markedly superior to that of an exact one. And in the result of EI Centro, the shape of three type response spectra is similar, further confirmed the accuracy and reliability of the cosine transform method.