Carbon structures have been shown to be potentially efficient hydrogen storage media, but the micro adsorption/diffusion kinetic properties of hydrogen storage are still unclear. We investigated the adsorption of H2 in carbonaceous nanoporous by molecular dynamics simulations. It was found that the hydrogen molecules were completely adsorbed when the pore size was 1 nm, and existed in both adsorbed and free forms when the pore size was 2–6 nm, and the adsorption was in a saturated state, with the absolute adsorption amount keeping constant. Modification of functional groups on the inner side of graphene pores reduces the hydrogen storage capacity, and this effect becomes more and more obvious with decreasing pore size, especially for 1 nm pores. The total adsorption amount of H2 in 1 nm graphene pores was 0.01315 × 10−3 mol/m2, which was 3.8846 times that of graphene oxide pore. The hydrogen adsorption effect on different surfaces is: G > GO(-O-) > GO(-OH) > GO(-O-/OH). The results of this study are helpful to further understand the physical adsorption mechanism of molecular hydrogen on carbonaceous materials.