In this study, the non-equilibrium molecular dynamics simulation (NEMD) has been used to evaluate the thermal properties, especially the recti cation of ultra-narrow edge-functionalized graphene with hydrogen atoms. The system's small width equals 4.91 Å (equivalent to two hexagonal rings). The dependence of the thermal recti cation on the mean temperature, hydrogen concentration, and temperature difference between the two baths was investigated. Results reveal that the thermal recti cation increases up to 100% at 550 K by increasing the mean temperature. Also, it is disclosed that hydrogen concentration plays a vibrant role in thermal recti cation. Furthermore, a thoroughgoing recti cation is obtained in the half fully hydrogenated system due to maximum phonon scattering at the interface. Furthermore, the effects of temperature difference of baths ΔT on thermal recti cation has been calculated. As a result, the thermal recti cation decreases even though the current heat increases with ΔT. Finally, the thermal resistance at the interface using a mismatching factor between the twophonon density of states (DOS) on both sides of the interface has been explained.