A series of non-aqueous electrolytes were prepared by dissolving lithium bis(trifluoromethylsulfonyl)amide (LiTFSA) in triglyme and tetraglyme (Gx, x = 3 and 4), respectively, with varied molar ratios. With the electrolytes the cycling performance of Li-O2 batteries showed a strong dependence on the molar ratios between LiTFSA and Gx. It was found that the molar ratio of 1 to 5 was critical for the cycling-performance of Li-O2 batteries. High stability over 20 discharge–recharge cycles at 500 mA/gcarbon and in an O2 flow was obtained in LiTFSA-(Gx)5 (x = 3 and 4). The discharge product at cathode could be directly detected and identified as the dominant crystalline product Li2O2 on the 1st and 20th discharged electrodes using X-ray diffraction technique (XRD), which indicates rechargeability and feasibility of the electrolytes LiTFSA-(Gx)5 (x = 3 and 4) for Li-O2 batteries. At 1000 mA/gcarbon their capacities could be stabilized for 10 cycles. To our knowledge, this behavior of dependence of cycling performance of Li-O2 batteries on the concentration of Li salts is presented here for the first time, and it may be extended to other Li salts and solvents and suggest a new route for screening cycling-stable electrolytes for Li-O2 batteries.