Multiple-band terahertz filter device consisting of two different-sized metallic split rings with the nested design method is proposed and investigated in this paper. Five separated filtering resonant dips having different resonance amplitudes and quality factors are gained, which are mainly attributed to the hybrid coupling effect between the two nested split-ring resonators. More importantly, the resonance features of the five filtering dips show a significant dependence on the designed parameters, especially the gap between two nested split rings. The multiple-band filtering resonance device given here can open up new avenues to control terahertz waves in many technology-related fields.