A new geometrical vision for a graphene-based THz wave absorber is investigated in this work. A high-performance THz absorber is proposed to exploit complementary conventional periodic arrays of graphene disks. The equivalent circuit model is modified to take account of the complement pattern. The absorber works in two different operational modes based on chemical potential values. One mode shows absorption around 1 THz while the other one expresses perfect absorption at 6 THz and 9 THz. Such a considerable shifting ability via gate stimulations makes the proposed absorber an ideal block for reconfigurable metasurface. The comparison between the circuit model and full-wave simulation verifies an excellent match while ample sensitivity analysis are reported to show the reliability of the proposed switchable THz absorber.