Abstract: Based on the theory of local resonance, seismic metamaterials can break through the structure size limit and achieve the effective control of low frequency surface waves. A cross-shaped metamaterial structure is proposed to protect civil infrastructures against seismic damage. Firstly, the band gap structure and the vibration modes of each band gap boundary of the metamaterial unit are calculated and analyzed by using the finite element method, and the mechanism of the bandgap generation is clarified. Secondly, the transmission performance of surface waves incidents on the barrier structure is analyzed to verify the accuracy of the band gap. In addition, the metamaterial structure still has a certain attenuation effect outside the band gap because the structural units outside the band gap can produce local resonance phenomenon. Subsequently, the influences of the element structure sizes and material properties on the band gap are investigated. On this basis, positive and inverse gradient barrier structures are designed, and dynamic time history analysis is performed based on EI-Centro and other seismic waves. The results show that the proposed cross-shaped metamaterial structure has a wide band gap with 2 Hz covered, which is the primary frequency at which earthquakes cause structural damage, and the band gap range is easy to handle; after the positive and inverse gradient arrangement, the low frequency surface wave energy is absorbed in the band gap by means of "rainbow capture" and mode conversion; it has good attenuation effect on seismic waves such as EI-Centro, with the maximum acceleration amplitude attenuation being more than 80%; it also has engineering practical value, which provides a reference for the application of seismic metamaterials in the field of vibration isolation.