We proposed a far-infrared tunable metamaterial absorber using vanadium dioxide (VO2) and graphene as controlling materials. The properties of the absorber are investigated theoretically using the finite-difference time-domain (FDTD) technique. It was found that when the Fermi energy level of graphene is fixed at zero, VO2 is in the insulated state, and the metasurface exhibits far-infrared broadband absorption performance, with absorptance exceeding 90% in the wavelength range of 12.6 μm to 23.2 μm. In addition, by elevating the Fermi energy level of graphene, the absorption bandwidth of the device is expanded continuously. When the VO2 is in the metallic state, the device can flexibly transform into a far-infrared narrowband absorber. The device also has the advantage of being insensitive to changes in polarization and incident angle. The origin of the absorption and the tuning principle of the device were analyzed and verified successfully by using an equivalent circuit model (ECM). Besides, we also studied the refraction index sensing characteristics of the absorber. Surprisingly, the absorber exhibits excellent sensing characteristics, and its sensitivity (S) reaches 14.108 μm per RIU and the figure of merit (FOM) is 6.13 per RIU.