The geometry, stability, and electronic properties of Con (n =1~5) clusters and ConO2 clusters are calculated by density functional theory (DFT) with Dmol3 program by using the generalized gradient approximation PBE functionals. ConO2 clusters are constituted by adsorption of Con (n = 1~5) clusters and molecular oxygen (O2) (vertical and parallel method). The results verify that the binding energy of Con clusters increases with the increase in the number of clusters, and the changing trend tends to be gentle with increasing stability. The adsorption stability, Co—O bond length, O—O bond length, and charge transfer of molecular oxygen at the top site, bridge site, and hole site of the Con clusters show regular changes, indicating that molecular oxygen is activated. The more charge transfer from Con cluster to molecular oxygen, the stronger interaction and the bigger adsorption and binding energy. The adsorption energy and binding energy of the Co2O2 B clusters with molecular oxygen vertical adsorption type are the strongest, which are -6.744 eV and 4.611 eV, respectively, and the obtained charge of molecular oxygen is -1.130 e.