The present work describes a theoretical investigation of the near-field thermal radiation be-tween semi-infinite media covered with a monolayer of graphene. Doped Si, SiC-based metamaterial, and SiC are used as the substrate medium. It is found that the radiative heat flux can be either enhanced or suppressed by introducing graphene layer. Given that the permittivity of doped Si depends on doping concentration, the mechanism of the enhancement and the reduction of heat flux by insertion of graphene can be explored through varying the permittivity of doped Si substrate. Graphene can enhance the heat flux if it matches resonance frequencies of surface polaritons at vacuum-source and vacuum-receiver interfaces. Further, the heat flux significantly increases if original substrate does not support surface polaritons. Although graphene rarely affects the magnetic surface polaritons of SiC-based metamaterial, it enhances the heat flux through the interaction with the electric surface polaritons of the substrate. The results obtained in this dissertation provide an important guideline into enhancing and suppressing the near-field thermal radiation between semi-infinite media.