Graphene quantum dots (GQDs), which is the latest addition to the nanocarbon material family, promise a wide spectrum of applications. Herein, we demonstrate two different functionalization strategies to systematically tailor the bandgap structures of GQDs whereby making them snugly suitable for particular applications. Furthermore, the functionalized GQDs with a narrow bandgap and intramolecular Z-scheme structure are employed as the efficient photocatalysts for water splitting and carbon dioxide reduction under visible light. The underlying mechanisms of our observations are studied and discussed.