In this paper, we have investigated an absorber based on two-dimensional hexagonal graphene array and theoretically propose a calculation method for the approximate conductivity of graphene in the terahertz band and its correction term, and we also theoretically explain the phenomenon of blue-shift of the absorption spectrum with increasing graphene chemical potential. The finite difference time domain (FDTD) method shows that this absorber has the advantages of exciting high absorption rate, multi-band, tunable and high figure of merit (FOM). By discussing the analysis of different graphene geometries, we demonstrate the optimality of this result. The bottom layer of our absorber is composed of an Au reflection layer, and the middle layer is a silicon oxide dielectric layer. Four hexagonal two-dimensional graphene is placed at the top. Taking this as the basic unit, an array can be formed. Our absorber has a simple structure, which simplified the processing technology and saves the processing cost greatly. In the near-infrared band from 1600 nm to 1900 nm, our absorbers have absorption peaks of 99.70%, 99.25% and 99.82% at 1667.19 nm, 1691.71 nm and 1773.20 nm, respectively. In addition, the resonance wavelength of the absorber can also be adjusted by adjusting the chemical potential and refractive index of the silicon dioxide layer. The absorber also has the features of polarization and angular insensitivity. Our simulation results show that our absorber's absorption spectrum will change significantly as the ambient refractive index changes, and based on this, we can calculate the sensitivity and the figure of merit (FOM) of our model. We finally calculated the best FOM for the three peaks of our absorber (sorted by resonance wavelength from short to long) is 90.93, 90.96, 107.34, and the sensitivity is 290.25 nm/RIU, 309.95 nm/RIU, 318.50 nm/RIU, respectively. Thus, we trust that our absorbers can be widely used in Near-infrared thermal radiation, optical detector and Near-infrared sensors.