In this paper, an absorber with multi-band, tunable, high Q, and high sensitivity, based on terahertz periodic two-dimensional patterned graphene surface plasmon resonance (SPR), is proposed. The absorber consists of a bottom metal film separated by a periodically patterned graphene metamaterial structure and a SiO2 dielectric layer, where the patterned graphene layer is etched by “+” and “L” shapes and circles. It has simple structural features that can greatly simplify the fabrication process. We have analyzed the optical properties of a graphene surface plasmon perfect metamaterial absorber based on graphene in the terahertz region using the finite-difference method in time domain (FDTD). The results show that the absorber device exhibits three perfect absorption peaks in the terahertz bands of f1 = 1.55 THz, f2 = 4.19 THz, and f3 = 6.92 THz, with absorption rates as high as 98.70%, 99.63%, and 99.42%, respectively. By discussing the effects of parameters such as the geometrical dimensions of patterned graphene metamaterial structure “+” width W1, “L” width W2, circular width R, and the thickness of the dielectric layer on the absorption performance of absorber, as well as investigating the chemical potential and relaxation time of patterned-layer graphene material, it was found that the amplitude of the absorption peaks and the frequency of resonance of absorber devices can be dynamically adjusted. Finally, we simulated the spectra as the surrounding refractive index n varied to better evaluate the sensing performance of the structure, yielding structural sensitivities up to 382 GHz/RIU. Based on this study, we find that the results of our research will open new doors for the use of multi-band, tunable, polarization-independent metamaterial absorbers that are insensitive to large-angle oblique incidence.