A sub-wavelength periodic composite structure with square frame and hollow cylinder nested by Au is proposed. The finite difference time domain algorithm is used to simulate the composite structure. It is found that the minimum transmittance can reach 7.46%, the minimum full width at half maxima can reach 7.25 nm, the maximum reflectivity is 87.61%, and the maximum absorptivity is 38.00%, when the wavelength is 400?900 nm. It is found that the resonant mode of the composite structure is coupled by the resonant mode of the two basic structures, and the nested mode can further reduce the transmission of single structure and increase the interaction between light and composite structure. By changing the parameters of the composite structure, a wide and efficient control range of plasmon and a narrow transmission spectrum are obtained. This provides theoretical guidance for the design of artificial subwavelength periodic composite structures.