Numerical simulations based on solving the Maxwell equations provide a robust and efficient approach to obtaining optical properties of plasmonic metal nanoparticles (NPs), but they have high computational costs when considering the real conditions of incorporated NPs such as random distribution and nonuniform size. Therefore, an effective medium theory, taking into account light scattering on the surface of NPs and light concentration by localized surface plasmon resonance, has been employed to obtain optical properties of randomly embedded spherical NPs with nonuniform radii into GaAs. The results are input into an optoelectrical model of graphene/GaAs Schottky barrier solar cells (SCs), calibrated by the experimental data, to compare the performance of plasmonic graphene/GaAs SCs with the incorporation of different metal NPs of Au, Ag, Al, and Cu. Furthermore, the effects of the number of graphene layers, the radius of NPs, and the amount of size dispersion on the photovoltaic parameters of plasmonic graphene/GaAs SCs have been investigated. It is demonstrated that increasing the radius and size dispersion of NPs, by inducing an inhomogeneous broadening and an increase of plasmon band amplitude, enhances the efficiency of plasmonic graphene/GaAs SCs.