The oxygen–containing functional groups of graphene oxide (GO) play an important role in hydrogen storage. In addition to the contribution of the specific surface area and micro–porous porosity, the interactions of the functional groups with H₂ molecules are also an important factor in the aspect of GO hydrogen storage. This paper explores the oxygen–containing functional groups affecting the hydrogen physisorption capacity of the GO and reduced graphene oxide (RGO) by experimental H₂ adsorption measurement and theoretical calculation. Experimental results related to synthesis of GO and RGO via the modified Hummer's method and characterized using SEM, TEM, SAED, XRD, FTIR, TGA and Raman spectroscopy, are presented. Compared with RGO, the surface and edge of GO contain a large amount of oxygen–containing functional groups and its specific surface area is slightly increased through BET measurement. GO is found to exhibit better H₂ uptake capacity (0.74 wt%) as compared to RGO (0.47 wt%) at 77 K and pressure up to 10 bars. The density functional theory is applied to optimize the adsorption configurations of H₂ on the surface of samples. Calculation results show that the adsorption on the GO can be promoted by surface functional groups epoxy, hydroxyl, carboxyl and carbonyl; the enhancement of hydroxyl is greater than other species on the surface and the maximal adsorption energy reaches to −0.112 eV which is about twice that of graphene. As indicated above, these functional groups could be formed easily on the graphene surface, which not only enhance specific surface area and interlayer spacing, but also significantly change the location of carbons, redistributing the electron structure of graphene and enhancing the adsorption energy.