In this study, density functional theory was used to investigate the effect of adsorption process and interaction between methanol as a fuel and graphene as a catalyst. Thermodynamic studies in this field have shown that Gibb's free energy is positive in most cases. Therefore, adsorption of methanol on graphene is very low and in the physical mode. Thus, other ways are required to increase adsorption on graphene surface. Changing pristine graphene (PG) to vacancy graphene (VG) or N-doped graphene (NG) can increase absorption, and convert their adsorption into chemical adsorption. Vacancy and N-doped in electronic structure of graphene increase adsorption of methanol to graphene. Increased absorption of VG and NG, in addition to changes in charge transfer causes significant changes in the location of HOMO and LUMO, which was confirmed by adsorption energy, NBO, QTAIM, and DOS.