Periodic DFT calculations were carried out to investigate the mechanism of methane oxidation with H2O2 over the defined Fe sites in Fe/ZSM-5 zeolite. The initial Fe site is modelled as a [(H2O)2Fe(III)(μO)2Fe(III)(H2O)2]2+ extra-framework cluster deposited in the zeolite pore charge-compensated by two anionic lattice sites. The activation of this cluster with H2O2 gives rise to the formation of a variety of Fe(III)-oxo and Fe(IV)-oxo complexes potentially reactive towards methane dissociation. These sites are all able to promote the first C-H bond cleavage in methane by following three possible reaction mechanisms, namely, the (a) heterolytic and (b) homolytic methane dissociation as well as Fenton-type involving free OH radicals as the catalytic species. The C-H activation step is followed by the formation of MeOH and MeOOH and the regeneration of the active site. The Fenton-type path is found to proceed with the lowest activation barrier. Although the barriers for the alternative heterolytic and homolytic pathways are found to be somewhat higher, they are still quite favourable and expected to be feasible under reaction conditions, resulting ultimately in MeOH and MeOOH products. H2O2 oxidant competes with CH4 substrate for the same sites. Since the oxidation of H2O2 to O2 and two [H+] is energetically more favourable than the C-H oxo-functionalization, the overall efficiency of the latter target process remains low.