Methanol oxidation efficiency and resistance to CO poisoning are the most challenging issues of direct methanol fuel cells. Much experimental effort has been made, such as generating Pt-based binary and ternary nanoparticles, creating composite substrates, and fabricating nanoparticles with special shapes to overcome drawbacks. Our previous experiment showed that the ternary PtRuM₃/C-MWCNTs (M = Fe, Co) electrocatalysts, C-MWCNTs = carbon Vulcan-multiwalled carbon nanotubes composite, exhibited the high methanol oxidation activity and tolerance to CO poisoning. However, the reaction mechanisms on the ternary PtRuM₃/C-MWCNTs (M = Fe, Co) electrocatalysts remain unknown. Therefore, this work is devoted to elucidating the problem using the density functional theory calculations and thermodynamic model. Our present study showed that the methanol oxidation proceeds via four possible reaction pathways on the surface of PtRuM₃/C-MWCNTs, where the most favourable one follows a series of steps converting CH₃OH  CH₃OH*  CH₂OH*  CH₂O*/CHOH*  CHO*  CHOOH*  CHOO*/COOH*  CO₂* with the thermodynamic barrier of 0.513 eV for both applied potentials of U = 0 V and 1.005 V on PtRuFe₃/C-MWCNTs, and 0.404 eV for U = 0 V and 0.167 eV for U = 1.005 V on PtRuCo₃/C-MWCNTs. We also clarified the physical insights into the interaction between the methanol oxidation intermediates with the substrates’ surface via analysing electronic properties. The results of this study should be useful for rationally designing the anode of the fuel cells.