The reburning process in a furnace, a key way to reduce NOx emissions, is a heterogeneous reaction during coal combustion, in which the heterogeneous adsorption is dominant. Zhundong coal with a high content of alkali metal can enhance the reburning process. In this paper, the influence of sodium and a defect on NO heterogeneous adsorption was studied by the density functional theory, and the thermodynamic characteristic was also analyzed. The results indicate that the binding energy for NO adsorption on the pristine graphene surface (graphene-NO), Na-decorated pristine graphene surface (graphene-Na-NO), defect graphene surface (gsv-NO) and Na-decorated defect graphene (gsv-Na-NO) is −5.86, −137.12, −48.94 and −74.85 kJ/mol, respectively, and that the heterogeneous adsorption is an exothermic reaction. Furthermore, except for covalent bonds of C and N, C and O for gsv-NO, other interactions are a closed-shell one, based on the analysis of AIM, ELF and IGM. The area of electron localization for NO is graphene-Na-NO > gsv-Na-NO > gsv-NO > graphene-NO. The dispersion interaction is the main interaction force between NO and the pristine graphene surface. The δg index for the atom pairs about N–C and O–C on the pristine graphene surface is also the smallest. The density of spikes at graphene-Na-NO is bigger than that at gsv-Na-NO. Moreover, the thermodynamics characteristic showed that the reaction equilibrium constant of graphene-NO is less than those on the other surfaces under the same temperature. Thus, NO on the pristine graphene surface is the most difficult to adsorb, but the presence of sodium and a defect structure can promote its adsorption.