Density functional theory calculations are performed to investigate the role of lithium salts regarding the oxygen reduction reaction (ORR) occurred in non-aqueous electrolyte in Li-air batteries. This study is useful to elucidate the influence of ion-conducting lithium salts on ORR kinetics. The Li+-O bonding, binding energy, Gibb's free energy, heat of formation energy, and IR spectra with increase in dimethyl sulfoxide (DMSO) solvent molecules in the primary solvation shell reveal that lithium trifluoromethanesulfonate (LiCF3SO3) is the most stable in dimethyl sulfoxide (DMSO) as compared to lithium hexafluorophosphate (LiPF6) and lithium bis(trifluoromethanesulfonimide (LiN(CF3SO2)2). Infrared spectroscopic (IR) data confirm the formation of lithium peroxide (Li2O2), lithium oxide (Li2O), and lithium carbonate (Li2CO3) as discharge products on the micro-electrode surface in non-aqueous electrolyte containing lithium salts. The infrared (IR) analysis reveals that the lithium trifluoromethanesulfonate/dimethyl sulfoxide (LiCF3SO3/DMSO) electrolyte is primarily assumed to be the most favorable for ORR kinetics. In order to study the kinetics of oxygen reduction reaction at the oxygen cathode of non-aqueous Li-air battery with three Li salts in dimethyl sulfoxide (DMSO), we calculate thermodynamic properties of the reactions held during the formation of lithium peroxide (Li2O2) and lithium oxide (Li2O). The Gibb's energy and heat of formation of these reactions indicate that lithium trifluoromethanesulfonate/dimethyl sulfoxide (LiCF3SO3/DMSO) electrolyte plays a key role in oxygen reduction reaction mechanism compared to other two.