The chemical repair of radical-damaged DNA by glutathione in aqueous solution has been studied using density functional theory. Two main mechanisms were investigated: the single electron transfer (SET) and the hydrogen transfer (HT). Glutathione was found to repair radical damaged DNA by HT from the thiol group with rate constants that are close to the diffusion-limited regime, which means that the process is fast enough for repairing the damage before replication and therefore for preventing permanent DNA damage. The SET mechanism was found to be of minor importance for the activity of glutathione. In addition while SET can be essential for other compounds when repairing radical cation species, repairing the C'-centered guanosyl radicals via SET is not a viable mechanism, due to the very low electron affinity of these species. The importance of considering pH-related physiological conditions and using complex enough models, including the ribose moiety and the H bonding between base pairs, to study this kind of systems is discussed.