In recent years, research on the dynamic regulation of electromagnetic wave absorbers using graphene has attracted extensive attention. In this paper, a patterned graphene absorber is designed with a catenary, and the calculated results show that the absorber achieves perfect dual-frequency absorption at 5.57 THz and 7.11 THz in the terahertz frequency band in the TE wave mode. The analysis of the electric field strength and current distribution on the surface of the graphene layer shows that the perfect absorption of the dual frequency is related to the electric dipole resonance caused by the local surface plasmon excitation of the graphene layer. On this basis, the simulation of the relationship between the resonant absorption frequency and the geometric parameters of the absorber structure, the coupled bias voltage and the incident angle shows that the absorber can effectively realize the dynamic control of the absorption, and the structure can also reflect the absorption rate of more than 90% for a large range of incidence angle (0° to 40°).