High oxygen radical stability of electrolyte solvent is a key parameter necessary to overcome a large voltage gap in discharge–charge profiles of the non-aqueous Li–air battery. We have proposed N-methyl-N-propylpiperidinium bis(trifluoromethansulfonyl)amide (PP13TFSA) as an appropriate candidate of the electrolyte solvent. PP13TFSA based Li–O2 cells enabled us to draw low charging voltage of around 3.3 V, lowering the voltage gap by nearly half in comparison with those of conventional carbonate-based cells (c.a. 1.4 V). Here, through the detailed analyses of discharge products, we verified the fact that the voltage gap was notably decreased by using the highly radical stable electrolyte solvent. TEM-EELS and FT-IR analyses indicated that Li2O2 was deposited as a discharge product. 13C NMR spectroscopy suggested that no decomposed species derived from electrolyte decomposition was observed from a discharged cathode. GC–MS analyses also revealed that CO and CO2 gases as indices of the decomposed species were not monitored at all. Above-described data substantiated a desirable discharge reaction, resulting in low charging voltage as well as small voltage gap. Design of electrolyte solvents based on their oxygen radical stability and full understanding of the cathode reaction mechanism contributed greatly to a dramatic improvement of the Li–air battery performances.