C1s X-ray photoelectron spectroscopy (XPS) spectra of graphene with two to eight pentagons and fullerene pentagons were simulated using density functional theory calculation. Peak shifts and full width at half maximum (FWHM) of calculated C1s spectra were compared with those of actual C1s spectra. Introduction of up to four isolated pentagons had no influence on shifts of the calculated peak maxima of graphene (284.0 eV), whereas the introduction of six or more pentagons shifted the calculated peak maximum toward low binding energies because the number of connected pentagons increased. The presence of pentagons also influenced FWHMs. Introduction of six pentagons increased the calculated FWHMs from 1.25 to 1.45 eV, whereas introduction of eight or more pentagons decreased the FWHMs. The FWHM reached at 1.15 eV by introducing twelve pentagons (fullerene). These calculated shifts and FWHMs were close to the actual shifts of graphite (284.0 eV) and fullerene (282.9 eV) and FWHMs of graphite (1.25 eV) and fullerene (1.15 eV). Based on the calculated and the actual results, we proposed peak shifts and FWHMs of graphene with the different number of pentagons, which can be utilized for analyzing actual XPS spectra. Proposed FWHMs can be adjusted by measuring actual FWHMs using each device.