The first-principles density functional theory calculations was used to investigate the performance of dual-atom catalysts (DACs) anchored on a Mo₂CO₂ MXene substrate (denoted as M₁M₂/Mo₂CO₂, where M₁=Fe,Co,Ni and M₂=Co,Ni,Cu) for the electrocatalytic conversion of methane (CH₄) to methanol (CH₃OH). The stability of the catalysts was assessed via formation energy and dissolution potential calculations. The catalytic activity and selectivity were probed through reaction free energy analysis. The origin of catalytic activity was elucidated via electronic structure analysis. It is found that the formation energy of M₁M₂/Mo₂CO₂ catalyst is from -4.44 eV to -2.62 eV, and the dissolution potential is between 1.03 V and 1.77 V, exhibiting excellent thermodynamic and electrochemical stability. Among them, the activation energy barrier of methane on CoCu/Mo₂CO₂ is only 0.05 eV, indicating excellent catalytic activity. Within a potential window of 0.74 V to 1.01 V (vs. RHE), this catalyst achieves methanol selectivity exceeding 99%. The catalytic activity shows a positive correlation with the charge ratio (q(M₁)/q(M₂) of the dual-metal centers. The high activity of CoCu/Mo₂CO₂ originates from its q(M₁)/q(M₂) ratio of 0.3, which is close to the theoretical optimum value.