We investigated the adsorption of Na on graphene and graphene oxide, which are used as anode materials in sodium ion batteries, using density functional theory. The adsorption energy for Na on graphene was -0.507 eV at the hollow sites, implying that adsorption was favorable. In the case of graphene oxide, Na atoms were separately adsorbed on the epoxide and hydroxyl functional groups. The adsorption of Na on graphene oxide-epoxide (adsorption energy of -1.024 eV) was found to be stronger than the adsorption of Na on pristine graphene. However, the adsorption of Na on graphene oxide-hydroxyl resulted in the generation of NaOH as a by-product. Using density of states (DOS) calculations, we found that the DOS of the Na-adsorbed graphene was shifted down more than that of the Na-adsorbed graphene oxide-epoxide. In addition, the intensity of the DOS around the Fermi level for the Na-adsorbed graphene was higher than that for the Na-adsorbed graphene oxide-epoxide.