Plasmonic antennas are attractive optical components of the optoelectronic devices, operating in the far-infrared regime for sensing and imaging applications. However, low optical absorption hinders its potential applications, and their performance is limited due to fixed resonance frequency. In this article, a novel gate tunable graphene-metal hybrid plasmonic antenna with stacking configuration is proposed and investigated to achieve tunable performance over a broad range of frequencies with enhanced absorption characteristics. The hybrid graphene-metal antenna geometry is built up with a hexagon radiator that is supported by the Al2O3 insulator layer and graphene reflector. This stacked structure is deposited in the high resistive Si wafer substrate, and the hexagon radiator itself is a sandwich structure, which is composed of gold hexagon structure and two multilayer graphene stacks. The proposed antenna characteristics i.e., tunability of frequency, the efficiency corresponding to characteristics modes, and the tuning of absorption spectra, are evaluated by full-wave numerical simulations. Besides, the unity absorption peak that was realized through the proposed geometry is sensitive to the incident angle of TM-polarized incidence waves, which can flexibly shift the maxima of the absorption peak from 30 THz to 34 THz. Finally, an equivalent resonant circuit model for the investigated antenna based on the simulations results is designed to validate the antenna performance. Parametric analysis of the proposed antenna is carried out through altering the geometric parameters and graphene parameters in the Computer Simulation Technology (CST) studio. This clearly shows that the proposed antenna has a resonance frequency at 33 THz when the graphene sheet Fermi energy is increased to 0.3 eV by applying electrostatic gate voltage. The good agreement of the simulation and equivalent circuit model results makes the graphene-metal antenna suitable for the realization of far-infrared sensing and imaging device containing graphene antenna with enhanced performance.