A three-layer construction was proposed to induce anomalous transmission response for a normal incidence of terahertz (THz) wave. This structure was composed of a dielectric layer of quartz and two metallic layers, which were deposited on the two surfaces of quartz and patterned the same periodic arrays of subwavelength air circular loop. Based on comparative analyses of dispersion relations of both the structure and its partial structures, propagating surface plasmon and localized surface plasmon principally dominated the lower and higher resonant peaks appearing in the calculated transmittance spectrum, respectively. A sample was fabricated by laser technology for experiment and the measured THz transmission showed a good agreement with simulation, providing reference for potential applications.