The advent of graphene has opened new avenues for the design of high-performance metamaterial devices, particularly in the realm of electromagnetic absorption applications. This paper introduces a novel design for a broadband tunable graphene metamaterial absorber (GMMA) utilizing graphene. Through numerical simulations, our proposed GMMA demonstrates a absorption bandwidth of 3 THz (1.14 -4.14 THz) with absorptivity exceeding 90% for both transverse magnetic (TM) and transverse electric (TE) modes. A comprehensive numerical analysis, using a transmission line equivalent circuit model, is conducted to find out the impedance components of all the corresponding layers, which can be significant to determine the impedance matching. The absorber exhibits wideband tunability, polarization insensitivity, and robust tolerance to structural variations, making it a promising candidate for diverse applications in the terahertz (THz) band especially in the antenna regime. Our proposed GMMA antenna can achieve a gain of 37.48 dB, a directivity of 32.81 dB, a return loss of -34 dB, and an efficiency of 99.96%. This research provides a valuable contribution to the development of tunable broadband GMMAs for THz frequencies, addressing the increasing demand for high-speed and efficient devices in the modern era of science and technology.