Selective C-H oxidation is thought to be a highly suitable strategy for building synthetic blocks and generating bioactive compounds. Noncovalent DNA catalysis for C-H bond cleavage is studied for the first time in order to delineate the so-called 'oxidation enhancement effect' on oxidatively generated damage in DNA duplex structures. Herein, DFT methods have been used to gain insight into the reactivity of the 5-hydroxy-6-peroxyl-5,6-dihydrothymine radical using ten single-stranded and duplex DNA models. Reliable M06-2X/6-31+G(d,p) calculations indicate that hydrogen bonding between the complementary base pairs significantly enhances the reactivity of the thymine peroxyl radical in duplex DNA models towards the C1'-H1' bond. An excellent linear relationship of the reaction activation barrier vs. the difference between the bond dissociation free energies (BDFE) of the C-H and O-H bonds is observed. With the noted role of charge transfer from LPO4' on 2-deoxyribose to its adjacent C1'-H1' anti-bonding orbital, a hyperconjugation effect is proposed to explain the reason why the barrier heights are close to each other for the studied duplex DNA models. The difference in the reactivity of the thymine peroxyl radical in the duplex and related single-strand DNA models is rationalized in terms of the preparatory energy and the optimal σC1'-H1' and oxyl-p based π*-orbital interactions.