Carbon materials attract much attention because of their possibility as effective hydrogen storages. In a hydrogen adsorption process, two steps of chemical reactions are expected; (i) dissociation of hydrogen molecules and (ii) adsorption of hydrogen atoms on carbon atoms. In this work, the hydrogen adsorbing mechanism on graphene surfaces has been analyzed using a combined method of molecular dynamics and first-principles calculations. As a result of those calculations, defects and distortions in graphene layers cause their peculiar electronic structures and generate a preferable conformation for hydrogen adsorption. It is suggested that first-principles calculations are available in order to treat chemical reaction systems because they actually represent charge transfers between each atom. Furthermore, atomic forces calculated using first-principles methods can be coupled to molecular dynamics simulations and the results of those simulations explains experimental observations. Consequently, activation energies for the hydrogen storage and discharge have been estimated 2.06 eV and 0.64 eV, respectively. This result suggests carbon materials such as graphene are preferable for a hydrogen storage material.