Graphitic carbon nitride (g-C₃N₄) is a promising semiconductor material which has been widely studied in nanoscience. However, the effect of modifying the performance of g-C₃N₄ is still under debate. In this communication, we show the size and functional group effects on the g-C₃N₄ using density functional theory (DFT) calculations. It was found that a molecule with six repeated g-C₃N₄ units (g-C₃N₄-6) could be the smallest unit that converges to the limit of its HOMO⁻LUMO gap. Calculations of g-C₃N₄-6 with varying numbers of substituted C≡N, C=O, and O-H functional groups show that C≡N and C=O could narrow down the HOMO⁻LUMO gap, while O-H could slightly raise the gap. This study shows that the change of substituents could tune the band gap of g-C₃N₄, suggesting that rationally modifying the substituent at the edge of g-C₃N₄-based materials could help to significantly increase the photocatalytic properties of a metal-free g-C₃N₄.