By now, the negative refraction phenomenon occurs only in the microwave band in the left-handed materials, and this frequency band is called resonant frequency band. The application of the left-handed materials is greatly limited because the resonant frequency is low, and the source of wave is usually sun light or visible light.How to shift the resonant frequency from low frequency to high frequency, even to the visible light band, is an important and urgent research problem. Many parameters of the periodic structures will greatly affect the resonant frequency, including the shapes and sizes. The resonant frequency is shifted by adjusting the cell size.The relation that the resonant frequency band can be shifted and broadened from low frequency to high frequency with the reducing cell size, is obtained by simulation and experiment.