The adhesion mechanism of epoxy resin (ER) cured material consisting of diglycidyl ether of bisphenol A (DGEBA) and 4,4'-diaminodiphenyl sulfone (DDS) to pristine graphene and graphene oxide (GO) surfaces is investigated on the basis of first-principles density functional theory (DFT) with dispersion correction. Graphene is often used as a reinforcing filler incorporated into ER polymer matrices. The adhesion strength is significantly improved by using GO obtained by the oxidation of graphene. The interfacial interactions at the ER/graphene and ER/GO interfaces were analyzed to clarify the origin of this adhesion. The contribution of dispersion interaction to the adhesive stress at the two interfaces is almost identical. In contrast, the DFT energy contribution is found to be more significant at the ER/GO interface. Crystal orbital Hamiltonian population (COHP) analysis suggests the existence of hydrogen bonding (H-bonding) between the hydroxyl, epoxide, amine, and sulfonyl groups of the ER cured with DDS and the hydroxyl groups of the GO surface, in addition to the OH-π interaction between the benzene rings of ER and the hydroxyl groups of the GO surface. The H-bond has a large orbital interaction energy, which is found to contribute significantly to the adhesive strength at the ER/GO interface. The overall interaction at the ER/graphene is much weaker due to antibonding type interactions just below the Fermi level. This finding indicates that only dispersion interaction is significant when ER is adsorbed on the graphene surface.