We present a numerical study of a high negative effective refractive index based actively tunable squared shaped graphene split ring resonator for far infrared frequency spectrum. Graphene split ring resonator (GSRR) structure is investigated for the different cases of the split rings. Tunability of the structure is controlled by varying the different chemical potential of the graphene sheet, which can be controlled by external potential. Transmission, Reflection and Absorption parameters are investigated to check the resonance response. At each and every point of resonance, highly negative refractive index is been observed. The proposed structure is producing the multiple short as well as large band resonance band over 1 THz to 2.5 THz frequency range for the different chemical potential that varies between 0.1 eV to 0.9 eV. The study results inferred that tunable properties of the GSRR structure can help to design the various photonics device such as sensor, modulator and polarizer, etc.