The removal of actinides from radioactive wastewater is an important subject with the continuous application of nuclear energy. All-electron density functional theory (DFT) calculations were carried out to understand the adsorption behaviors of actinyl ions on C60(OH)24 fullerenol in this work. The outer-sphere (OS) bonding mode is more stable than the inner-sphere one because of the formation of multiple hydrogen bonds in the OS mode. The actinyl(VI) ions can be more efficiently absorbed by fullerenol than actinyl(V) ones. The bonding nature of actinyl ions with C60(OH)24 was revealed by various electron density topological analyses. Multiple hydrogen bonds formed in the OS complexes show moderate bond strength with partial covalent nature and are responsible for their high stability. IR spectra were fingerprinted to distinguish the interaction modes of actinyl ions with C60(OH)24.