In this work we report a non-aqueous electrolyte that supports long-term operation of the Li/air battery in dry ambient environments based on a non-hydrolytic LiSO3CF3 salt and a low volatility propylene carbonate (PC)/tris(2,2,2-trifluoroethyl) phosphate (TFP) solvent blend. By measuring and analyzing the viscosity of PC/TFP solvent blends, the ionic conductivity of electrolytes, and the discharge performance of Li/air cells as a function of the PC/TFP weight ratio, we determined the best composition of the electrolyte is 0.2m (molality) LiSO3CF3 7:3wt. PC/TFP for Li/O2 cells and 0.2m LiSO3CF3 3:2wt. PC/TFP for Li/air cells. Discharge results indicate that Li/air cells with the optimized electrolyte are significantly superior in specific capacity and rate capability to those with baseline electrolytes. More interestingly, the improvement in discharge performance becomes more significant as the discharge current increases or the oxygen partial pressure decreases. These results agree neither with the viscosity of the solvent blends nor the ionic conductivity of the electrolytes. We consider that the most likely reason for the performance improvement is due to the increased dissolution kinetics and solubility of oxygen in TFP-containing electrolytes. In addition, the electrolyte has a 5.15V electrochemical window, which is suitable for use in rechargeable Li/air batteries.