Carbon dots (CDs) are a kind of popular carbon nanomaterials with many functional groups that can be used in catalysis. However, in terms of calculation and simulation, most researchers choose to simplify CDs to pure graphene (GR) or graphene doped with nitrogen, boron, oxygen, and other elements due to the complexity of the calculation. In this study, the effects of adsorption of some functional groups (carboxyl, amino, and hydroxyl) on the properties of graphene have been investigated through first-principles calculations. The calculated results suggest that the adsorbed carboxyl group on graphene is relatively unstable, while the amino and hydroxyl groups can form covalent bonds with carbon atoms on the graphene and capture some electrons. When the bifunctional groups are adsorbed on the para or ortho position, it is beneficial for enhancing their stability on the graphene. However, when the bi-functional groups are adsorbed on the meta position, it will reduce the stability of the functionalized graphene. This research is beneficial for evaluating the specific functional groups on the surface of CDs, and it has particular significance for the simulation and modeling of CDs.