High level ab initio and density functional calculations of the ground state potential energy profiles were carried out to study the mechanism of the ion-molecule reaction CH4+O-2(+)(X (2)Pi (g)) for four reaction channels: insertion of O-2(+) into the C-H bond of methane (INS), hydride abstraction from methane (HA), charge transfer (CT), and O-O cleavage path (OO) after INS process to give CH2OH++OH. Common to these channels are initial encounter complexes, and our calculations match very closely experimental estimates for binding energies. The INS channel proceeds through CH4OO+ and gives a deep minimum corresponding to the exothermic and metastable intermediate CH3OOH+. This species can easily eliminate H to give CH2OOH+, a product observed experimentally. For the slightly endothermic HA channel to give CH3++OOH, two pathways were found: a direct pathway (likely to dominate at higher collision energy) from the encounter complex via a HA transition state at 5.8 kcal/mol above the reactants, and an indirect pathway with a slightly smaller energy requirement consisting of elimination of OOH from the INS intermediate CH3OOH+. A transition state with a high energy requirement of 15 kcal/mol was found for O-O cleavage from CH3OOH+, consistent with the experimental finding that O-O cleavage occurs at high energies. It was also found that the seam of crossing between two potential surfaces is facilitated and therefore the CT channel is promoted by the O-O stretching and the methane deformation vibrations, again consistent with the experimental results.