The lithium–air battery, a powerful competitor to replace the traditional lithium-ion battery, has attracted increasing attention due to its extremely high theoretical energy density. However, its development is limited by the cathode and electrolyte properties, which should include high stability, conductivity, and electrocatalytic properties in oxygen-rich environments. Here, we employ a systematic first-principles study of Li–O2 discharge and charge reactions on the Co3O4-based cathode with the assistance of dimethyl sulfoxide (DMSO) electrolyte. The structure, stability, and electronic properties of different surface reconstructions of the Co3O4(100) facet are investigated. In addition, the mechanisms and thermodynamic overpotentials of multi-step reactions between Li+/e– and O2 are provided, where lithium suboxide products (Li2O2 or Li3O2) are formed on the different Co3O4(100) terminations. The solvation shell of Li+ components in explicit DMSO solvent is investigated through ab initio molecular dynamics simulations. In general, we find that the Co3O4(100)-O (oxidized) surface is the most stable one under standard conditions, and the stable Li+ solvation structure is found in a tetrahedral Li(DMSO)4+ shell in the DMSO-based electrolyte. Moreover, in the system of the Co3O4(100)-O cathode and DMSO electrolyte, the solution model pathway is energetically favorable for the Li–O2 discharge reaction. It provides a low constant overpotential of 0.17 V during a long-term discharging process, thus causing the final toroid Li2O2 formation on the cathode. During the charging process, an overpotential of 0.36 V is required to rapidly decompose Li2O2.