High-performance cathode catalysts are always desirable for nonaqueous lithium-oxygen (Li-O2) batteries. Using density functional theory calculations, the structural, electronic, and magnetic properties of SSX-Gr with different C/X ratios (X = H or F) are systematically studied. Then, a detailed mechanism on the dissociation of O2 and the migration of Li on the SSX-Gr is revealed, based on which C6X and C8X are confirmed as the potential candidates as cathode catalysts. The studies on reaction pathways suggest that the four-electron pathway is the more possible catalytic pathway for the selected SSX-Gr. The free energy diagrams for discharging and charging processes catalyzed by SSX-Gr reveal that C6F exhibits the highest application potential due to its considerably low oxygen reduction overpotential (0.83 V) and oxygen evolution overpotential (1.47 V). The extra spins induced by single-side functionalization endow graphene with the electrocatalytic activity.