The mechanisms for O2 reduction and H2O/H2O2 formation on Co-corrin and Co-porphyrin cathode surfaces of the proton exchange membrane fuel cell (PEMFC) systems have been studied by hybrid Hartree-Fock/density functional theory (B3LYP) calculations with the LANL2DZ basis set. The calculations show that the reduced Co-corrin with a single negative charge (Co-corrin-) is more reactive than the neutral Co-corrin and the doubly charged Co-corrin2-. Both O2 and O adsorptions are most stable on Co-corrin-, rather than Co-corrin or Co-corrin2-. The potential energy profiles show that the decomposition of O2 on both Co-corrin and Co-corrin- can take place energetically favorably without thermal activation. The formation of H2O and H2O2 are predicted to occur by two separate reaction paths: the HO path and the HOO path. The HO path with H2O as the predominant product on the reduced Co-corrin- surface, the energetically favored surface, under operational cathodic conditions, which is consistent with recent experimental findings, wherein the PEMFCs with pyrolyzed vitamin B12 containing Co-corrin as catalysts loaded at the cathode, can deliver up to 14.5 A cm-3 at 0.8 V with IR compensation. A similar calculation performed for a Co-porphyrin system shows a significantly less efficient O2 reduction, consistent with the experiment results of the PEMFC power output studies.