Extended red emission (ERE) is a broad feature in the spectral region of 500-900 nm commonly observed in a wide range of circumstellar and interstellar environments. Although the observational constraints for ERE are well established, definitive identifications of the carriers and associated processes complying with these constraints remain unanswered. We report a plausible two-step model involving far-ultraviolet (UV)-irradiated single-layer graphene (SLG), considered as large polycyclic aromatic hydrocarbons, to meet these constraints and supported by laboratory experiments. The far-UV-treated SLG, producing structural defects and graphene quantum dots, showed photoluminescence excitation spectrum extending from the far-UV to UV-visible region, hence meeting the requirements of far-UV light and high photon conversion efficiency. Furthermore, a photoluminescence band shifted from ∼585 to ∼750 nm for high-dose-exposed SLG agrees with the observed redshift of the ERE band in regions under a greater far-UV radiation density.