Periodic structure possesses distinct characteristics that can block some certain frequency waves propagate through the structure，which can be used to reduce the unwanted seismic waves in civil engineering. Base on the Bloch-Floquet theory，the dispersive relation and frequency band gaps，are theoretically presented and derived to validate the effectiveness of the periodic foundation. A numerical model of 1D periodic foundation is established to investigate the filtering effects of elastic waves. The dynamic response and filtering effects of a scaled three-storey steel frame with a 1D periodic foundation and concrete foundation are performed and compared through the numerical method and shaking table tests. Ambient vibration，earthquake ground motion and sine waves are applied as the input waves. The results show that the 1D periodic foundation can effectively reduce the dynamic response of the structure when the frequencies of the input waves fall into the frequency band gaps of the foundation. Conversely，the 1D periodic foundation cannot reduce the dynamic response of the structure when the frequencies of the input waves fall outside of the frequency band gaps. Consequently，the proposed periodic foundation can be used to block the seismic waves and mitigate the seismic response of the superstructures through adjusting the frequency band gaps enveloping the exciting frequencies of the waves.