Graphene is a promising candidate for broadband and high-speed photodetectors. Nevertheless, the weak optical absorption of graphene restricts the performance of graphene photodetectors. In this work, the integration of a graphene photodetector with plasmonic metasurface which consists of optical nanoantennas is theoretically and numerically investigated. Also, the suggested photodetector is analytically evaluated via transfer matrix model (TMM). The incorporation of plasmonic modified omega-shaped nanoantennas not only boosts the light-graphene interactions but also it reinforces the light absorption, remarkably. The suggested optical nanoantennas contribute to the near-field enhancement and increased optical performance of the photodetector in two ways. First, by employing the proposed nanoantennas, electric quadrupole and vertical dipole plasmon oscillations are excited which enhance the magnetic fields around the nanoantennas. Second, due to the excitation of localized surface plasmon resonances (LSPRs), electric fields are highly concentrated and confined in the nanoscale regions, nanogaps and edges of nanoantennas. Similarly, electric fields are also highly enhanced in the ring sections of the nanoantennas, located parallel to the incident light. The proposed photodetector has small footprint and its broadband and tunable absorption can be tailored by manipulating the geometrical parameters of the structure and chemical potential of graphene. A near-unity absorption peak with FWHM of 343 nm is obtained at the telecommunication wavelength of 1550 nm. Also, absorbed power in the graphene increases to 66% and an ultrahigh electric field enhancement of 1350 is achieved in the gaps of the nanoantenna. The proposed photodetector can have possible applications in the nano-biosensing, imaging, biomedical monitoring and optical communication systems.