Abstract：In order to improve the calculation accuracy and efficiency of the seismic response spectrum, we introduce the linear recursive filtering method(LRFM) to calculate the seismic response spectrum. We derive the general expression of the response spectrum, which is based on the single degree of freedom dynamic system equation. To verify the calculation accuracy and efficiency of this method, we use the synthetic sinusoidal simple harmonic wave as the system input to compare the results of response spectrum which are calculated by the LRFM, the Duhamel step-by-step integration method, the Newmark-β method and the analytical solution method (ASM), and verify the error comparing with the ASM. We prove that the calculation method of the LRFM has good stability and high efficiency. In order to further prove the effectiveness of this method in calculating the actual data, we select the acceleration data of strong earthquakes with different prominent periods and spectrum from the ESM strong earthquake database, and the response spectrum of the LRFM and ASM is compared and analyzed under different damping conditions. The results show that the LRFM is consistent with the ASM in calculating the velocity response spectrum. The calculation result of the acceleration response spectrum has some errors with the increase of the damping, but the overall calculation accuracy could meet the requirements. The LRFM proposed in this paper could quickly and efficiently calculate the response spectrum information, so it has great significance for the rapid assessment of seismic intensity characteristics of the site and the stress condition of engineering structure.