In this study, dyadic Green's functions (DGFs) for a partially filled rectangular waveguide in the presence of a graphene layer is derived in closed form using the Ohm-Rayleigh method and the method of scattering superposition. Having DGFs of a linear medium, the response of the structure to any arbitrary current distribution can be achieved. In this work, after a brief review on governing equations for graphene conductivity, the electric fields of the structure due to infinitesimal electric dipoles are obtained using the proposed DGFs in closed form. To show the efficiency and accuracy of the proposed method, the results are compared with the simulation results of commercial software, where excellent agreement is observed.