The major objective of this paper is to address a controversial binding sequence between nucleic acid bases (NABs) and C-60 by investigating adsorptions of NABs and their cations on C-60 fullerene with a variety of density functional theories including two novel hybrid meta-GGA functionals, M05-2x and M06-2x, as well as a dispersion-corrected density functional, PBE-D. The M05-2x/6-311++G** provides the same binding sequence as previously reported, guanine (G) > cytosine (C) > adenine (A) > thymine (T); however, M06-2x switches the binding strengths of A and C, and PBE-D eventually results in the following sequence, G > A > T > C, which is the same as the widely accepted hierarchy for the stacking of NABs on other carbon nanomaterials such as single-walled carbon nanotube and graphite. The results indicate that the questionable relative binding strength is due to insufficient electron correlation treatment with the M05-2x or even the M06-2x method. The binding energy of G@C-60 obtained with the M06-2x/6-311++G(d,p) and the PBE-D/cc-pVDZ is -7.10 and -8.07 kcal/mol, respectively, and the latter is only slightly weaker than that predicted by the MP2/6-31G(d,p) (-8.10 kca/mol). Thus, the PDE-D performs better than the M06-2x for the observed NAB@C-60 pi-stacked complexes. To discuss whether C-60 could prevent NABs from radiation-induced damage, ionization potentials of NABs and C-60 and frontier molecular orbitals of the complexes NABs@C-60 and (NABs@C-60)(+) are also extensively investigated. These results revealed that when an electron escapes from the complexes, a hole was preferentially created in C-60 for T and C complexes, while for G and A the hole delocalizes over the entire complex, rather than a localization on the C-60 moiety. The interesting finding might open a new strategy for protecting DNA from radiation-induced damage and offer a new idea for designing C-60-based antiradiation drugs.