MXene is a variety of new two-dimensional (2D) materials with early transition metal carbides, nitrides, and carbonitrides. Quantum chemical studies have been carried out on the geometries, electronic structures, stability and catalytic properties of a non-noble metal single-atom catalyst (SAC) with single Co atom anchored on MXene materials of Mo 2 CS 2. The Co adatom anchored on top of the Mo atom of this MXene is found to be rather stable, and this SAC is appropriate for CO oxidation. The charge transfers from the surface to the adsorbed CO and O 2 play a significant role in the activation of these molecules on Co 1 /Mo 2 CS 2. With this catalyst, the Eley-Rideal (ER), Langmuir-Hinshelwood (LH), and Termolecular Eley-Rideal (TER) mechanisms are explored for CO oxidation. We find that, while all the three mechanisms are feasible at low temperature, Co 1 /Mo 2 CS 2 possesses higher catalytic activity for CO oxidation through the TER mechanism that features an intriguing OC(OO)CO intermediate (IM) adsorbed on Co single atom. The calculated activation energy barriers of the rate-limiting step are 0.67 eV (TER), 0.78 eV (LH) and 0.88 eV (ER), respectively. The present study illustrates that it is promising to develop and design low-cost, non-noble metal SACs using MXene types of 2D materials.