This paper introduces a novel plasmonic perfect absorber tailored for the terahertz frequency range, utilizing a single-mode configuration. The absorber architecture comprises a meticulously designed layered periodic array, combining SiO2, gold, and graphene components. The fundamental building block of this structure encompasses four strategically positioned L-shaped graphene patches and gold rods, placed on a SiO2 substrate. The absorption efficiency is further enhanced by incorporating an underlying gold layer functioning as a reflector. Employing the 3D finite difference time domain (FDTD) method, we rigorously investigate the absorption characteristics inherent to the proposed design. A comprehensive parametric study is conducted, varying the gold rod thickness and absorber geometry to optimize the absorption performance. Remarkably, our simulations reveal a conspicuous absorption peak exhibiting near-perfect absorbance, attaining 99.99%, precisely localized at 2.95 THz. Furthermore, the absorber's absorption frequency can be dynamically tailored by modifying the chemical potential of the graphene, a manipulation readily achieved through external bias voltage variation. The study provides illuminating insights into the electric and magnetic field distributions, elucidating the underlying absorption mechanisms. The results are later interpreted to discuss the effect of gold rods and graphene patches. The proposed graphene-based absorber seems to be a promising candidate for diverse applications encompassing sensors, modulators, detectors, and beyond.