The band gap properties of graphene quantum dots (GQDs) arise from quantum confinement effects and differ from those in semimetallic graphene sheets. Tailoring the size of the band gap and understanding the band gap tuning mechanism are essential for the applications of GQDs in opto-electronics. In this study, we observe that the photoluminescence (PL) of the GQDs shifts due to charge transfers between functional groups and GQDs. GQDs that are functionalized with amine groups and are 1-3 layers thick and less than 5 nm in diameter were successfully fabricated using a two-step cutting process from graphene oxides (GOs). The functionalized GQDs exhibit a redshift of PL emission (ca. 30 nm) compared to the unfunctionalized GQDs. Furthermore, the PL emissions of the GQDs and the amine-functionalized GQDs were also shifted by changes in the pH due to the protonation or deprotonation of the functional groups. The PL shifts resulted from charge transfers between the functional groups and GQDs, which can tune the band gap of the GQDs. Calculations from density functional theory (DFT) are in good agreement with our proposed mechanism for band gap tuning in the GQDs through the use of functionalization.