This paper presents a novel plasmonic graphene absorber designed for the terahertz frequency range, utilizing a dual mode optical filter configuration. The absorber consists of a layered periodic array comprising gold, SiO₂ and graphene. Key components include a graphene disk and four strategically positioned graphene stripes on a SiO₂ substrate. An underlying gold layer enhances the absorption efficiency by serving as a reflector. The structure is numerically simulated using the 3D finite difference time domain (FDTD) method. A comprehensive parametric study has been conducted to optimize the absorber's performance. The simulation results demonstrate near perfect absorption at 4.16 THz and 5.88 THz. This innovative design enables efficient absorption of terahertz radiation due to the plasmonic resonance effects of the graphene components. Additionally, the absorption frequency can be dynamically adjusted by altering the chemical potential of graphene through applying an external bias voltage. The tailored geometry and material composition result in a compact absorber with high absorption values and tunability. Detailed performance analysis through numerical simulations demonstrates the absorber's potential for applications in sensing, imaging, and communication systems operating in the terahertz frequency range.