In this paper, a new configuration of seismic isolation foundation containing several concrete layers and some rubber blocks is proposed. The concrete layers and the rubber blocks are placed periodically to form a periodic foundation. To study the isolation ability of this new configuration of periodic foundation, an equivalent analytical model is established. For practical applications, two very useful formulas are obtained. Using these formulas, the low bound frequency and the width of the first attenuation zone can be directly approximated without the calculation of dispersion structure. This new configuration of seismic isolation foundation enjoys the first attenuation zone between 2.15 Hz and 15.01 Hz, which means that the components of seismic waves with frequencies from 2.15 Hz to 15.01 Hz cannot propagate upward in the foundation. To illustrate the efficiency of this seismic isolation foundation, the seismic responses of a 6-story frame with three different foundations are simulated. Numerical simulations show that the seismic responses of the structure with the periodic foundation are greatly attenuated as compared with those of the structure with no isolation base or with traditional rubber bearings