Graphene-based photodetectors have been caught in the spotlight of optoelectronics devices and they are significant candidates for tunable detectors. Unfortunately, little reports are presented for absorption enhancement in near-infrared range. Therefore, here, a graphene-based photodetector with plasmonic structure consisting of Silicon and SiO2 substrate, graphene layer, and metal nano-grating in near-infrared range is proposed. The optical absorption of graphene layer in this structure increases due to the occurrence of plasmonic effects and excitation of surface plasmon polaritons (SPPs) in metal and graphene interface. The optical response of the proposed structure is numerically simulated using the finite-difference time-domain (FDTD) method. To optimize the optical absorption of the structure, the effects of geometrical parameters, the chemical potential of graphene, the number of graphene layers, and the incident angle have been investigated. Based on numerical results, the absorption of monolayer graphene enhanced from 0.023 to nearly 0.70, even to a maximum value of 0.80 in three-layer graphene and the total absorption of optimized structure reached to about 0.98 at telecommunication wavelength (1.55 μm). Moreover, the absorption spectrum of the proposed structure can be tuned by either changing the geometrical parameters of nano-grating or chemical potential of graphene.