Studying the bonding nature of uranyl ion and graphene oxide (GO) is very important for understanding the mechanism of the removal of uranium from radioactive wastewater with GO-based materials. We have optimized 22 complexes between uranyl ion and GO applying density functional theory (DFT) combined with quasi-relativistic small-core pseudopotentials. The studied oxygen-containing functional groups include hydroxyl, carboxyl, amido, and dimethylformamide. It is observed that the distances between uranium atoms and oxygen atoms of GO (U-OG) are shorter in the anionic GO complexes (uranyl/GO(-/2-)) compared to the neutral GO ones (uranyl/GO). The formation of hydrogen bonds in the uranyl/GO(-/2-) complexes can enhance the binding ability of anionic GO toward uranyl ions. Furthermore, the thermodynamic calculations show that the changes of the Gibbs free energies in solution are relatively more negative for complexation reactions concerning the hydroxyl and carboxyl functionalized anionic GO complexes. Therefore, both the geometries and thermodynamic energies indicate that the binding abilities of uranyl ions toward GO modified by hydroxyl and carboxyl groups are much stronger compared to those by amido and dimethylformamide groups. This study can provide insights for designing new nanomaterials that can efficiently remove radionuclides from radioactive wastewater.