This paper deals with the dual- band response of double ring metal array structure and anti-double ring structure in a terahertz wave range. The two samples are complementary in structure and their responses in the terahertz band are also complementary. The double ring structure shows two absorption crests and the anti-double ring structure shows two corresponding peaks at the same frequencies. The inner ring of the double ring structure is a source of high-frequency response, while the outer ring leads to the low-frequency vibration. Therefore, we can change the inner and the outer ring size respectively to control the terahertz response. And this response is unaffected by the period of the structure. The double ring structures provide a new method to produce multi-frequency terahertz resonator.