The entire reaction pathway for the gas-phase methane-methanol conversion by late transition-metal-oxide ions, MnO+, FeO+, and CoO+, is studied using an ab initio hybrid (Hartree-Fock/density-functional) method. For these oxo complexes, the methane-methanol conversion is proposed to proceed via two transition states (TSs) in such a way MO+ + CH4 --> OM+(CH4) --> [TS1] --> HO-M+-CH3 --> [TS3] --> M+(CH3OH) --> M+ + CH3OH, where M is Mn, Fe, and Co. A crossing between high-spin and low-spin potential energy surfaces occurs both at the entrance channel and at the exit channel for FeO+ and CoO+, but it occurs only once near TS2 for MnO+. The activation energy from OMn+(CH4) to HO-Mn+-CH3 via TS1 is calculated to be 9.4 kcal/mol, being much smaller than 22.1 and 30.9 kcal/mol for FeO+ and CoO+, respectively. This agrees with the experimentally reported efficiencies for the reactions. The excellent agreement between theory and experiment indicates that HO-M+-CH3 plays a central role as an intermediate in the reaction between MO+ and methane and that the reaction efficiency is most likely to be determined by the activation energy from OM+(CH4) to HO-M+-CH3 via TS1. We discuss in terms of qualitative orbital interactions why MnO+ (d(4) oxo complex) is most effective for methane C-H bond activation. The activation energy from HO-M+-CH3 to M+(CH3OH) via TS2 is computed to be 24.6, 28.6, and 35.9 kcal/mol for CoO+, FeO+, and MnO+, respectively. This result explains an experimental result that the methanol-branching ratio in the reaction between MO+ and methane is 100% in CoO+, 41% in FeO+, and < 1% in MnO+. We demonstrate that both the barrier heights of TS1 and TS2 would determine general catalytic selectivity for the methane-methanol conversion by the MO+ complexes.