Single-metal-atom catalysts supported on graphdiyne (GDY) exhibit great potential for catalyzing low temperature CO oxidation in solving the increasingly serious environmental problems caused by CO emissions due to the high catalytic activity, clear structure, uniform metal distribution and low cost. First principle calculations were employed to study CO oxidation activities of four M@GDY single-atom catalysts (M = Pt, Rh, Cu, and Ni). For each catalyst, five possible reaction mechanisms including bi-molecular and tri-molecular reactions were discussed. According to the calculated reaction barriers, the preferred reaction pathway is via the bi-molecular Langmuir-Hinshelwood (BLH) ((CO + O2)* → OCOO* → CO2 + O*) route to yield the first CO2 molecule with 0.55, 0.51, and 0.53 eV as the energy barriers of the rate-limiting steps of Pt@GDY, Rh@GDY, and Cu@GDY, respectively, whereas for Ni@GDY, it switches to the tri-molecular Eley-Rideal (TER1) ((2CO)* + O2→ OCOOCO* → 2CO2) mechanism with the reaction barrier of the rate-limiting step being 1.27 eV. Based on the energy difference in the initial states of the five reaction mechanisms, TER1 is generally viable. No matter it is based on the calculated reaction barrier or the energy of the initial state of each mechanism, the non-noble Cu@GDY is supposed to be an efficient catalyst as the noble ones. The electronic properties are calculated to explain the bonding strength and origin of the catalytic performance. The GDY support plays an important role in the electron transfer process.