The adsorption characteristics of H2 molecules on the surface of Pd-doped and Pd-decorated graphene (G) have been investigated using density functional theory (DFT) calculations to explore the sensing capabilities of Pd-doped/decorated graphene. In this analysis, electrostatic potential, atomic charge distribution, 2D and 3D electron density contouring, and electron localization function projection, were investigated. Studies have demonstrated the sensing potential of both Pd-doped and Pd-decorated graphene to H2 molecules and have found that the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), i.e., the HOMO-LUMO gap (HLG), decreases to 0.488 eV and 0.477eV for Pd-doped and Pd-decorated graphene, respectively. When H2 is adsorbed on these structures, electrical conductivity increases for both conditions. Furthermore, chemical activity and electrical conductivity are higher for Pd-decorated G than Pd-doped G, whereas the charge transfer of Pd-doped graphene is far better than that of Pd-decorated graphene. Also, studies have shown that the adsorption energy of Pd-doped graphene (−4.3 eV) is lower than that of Pd-decorated graphene (−0.44 eV); a finding attributable to the fact that the recovery time for Pd-decorated graphene is lower compared to Pd-doped graphene. Therefore, the present analysis confirms that Pd-decorated graphene has a better H2 gas sensing platform than Pd-doped graphene and, as such, may assist the development of nanosensors in the future.