Using the DFT calculations, the catalytic oxidation of CO by O2 is investigated over a Co atom decorated B36 cluster. Four different reaction pathways of the CO oxidation are investigated in details, namely, the Eley-Rideal (ER), the Langmuir-Hinshelwood (LH), the termolecular Eley-Rideal (TER), and new Eley-Rideal (NER). According to our results, the LH and TER mechanisms are the most energetically efficient routes for CO oxidation; however, the favored mechanism may be depending on the relative concentrations of CO and O2 molecules in the reaction mixture