The band gap characteristics of periodic structures provide a new idea for the field of seismic isolation in civil engineer? ing， among which the one-dimensional periodic foundation structure has garnered significant attention due to its simple structure and economical applicability. In this paper， by studying the vibration characteristics of the one-dimensional periodic base structure， an approximate analytical solution for calculating the one-dimensional rubber-concrete periodic base band gap is derived， and on this basis， a one-dimensional rubber-concrete periodic foundation optimization design method based on the resonance zone of the su? perstructure is proposed. Numerical examples in the frequency domain and time domain show that the periodic foundation designed by this optimization method can ensure a good damping effect of its superstructure in a wide and continuous frequency range.