This paper presents the first-principles investigation on interfacial adhesive strength between grafted polymer and cellulose. Focusing on maleic anhydride-grafted polypropylene, which is expected to be used in various applications including automobiles, a simple interfacial model was constructed under a local tensile loading condition. Then the stress-strain relation, deformation of molecular structure and breaking process were discussed. From comparison of mechanical responses among three chemically possible bonding configurations, it was clarified that the monoester bond exhibited higher interfacial strength than the diester bond. We also found that controlling the bonding configuration can improve the interface strength by about 50% compared to when primary OH groups react to form ester bonds. It was proved that this first-principles calculation model was effective for the definitive design and development of chemical modification of nanocellulose.