LiNi_0.8Co_0.1Mn_0.1O₂ positive-electrodes exhibit high discharge capacities about 200 mAh g^-1 by charging up to high potentials of ca. 4.3 V vs. Li/Li⁺. However, the reversible capacities gradually decrease upon repeated charge/discharge cycling in conventional electrolyte solutions due to 1) their oxidative decomposition at high potentials, 2) cracks of LiNi_0.8Co_0.1Mn_0.1O₂ powder, and 3) the phase transition to spinel/rock salt phases. The charge/discharge cycle performance of LiNi_0.8Co_0.1Mn_0.1O₂ was greatly improved in highly concentrated LiBF₄ propylene carbonate (PC) electrolyte solutions, which have low PC/Li⁺ molar ratios, such as nearly saturated 7.25 mol kg^-1 LiBF₄/PC (PC/Li⁺=1.35). However, the viscosity was much higher than that of conventional electrolyte solutions containing 1 mol dm^-3 Li salt. To reduce the viscosity, the highly concentrated LiBF₄/PC was diluted with fluorinated linear ether, 1,1,2,2–tetrafluoroethyl 2,2,3,3–tetrafluoropropyl ether (HFE). The dilution with HFE lowered both the viscosity and concentration of LiBF₄. A part of PC was replaced with low-viscosity dimethyl carbonate (DMC) to reduce the viscosity further. The charge and discharge properties of LiNi_0.8Co_0.1Mn_0.1O₂ were investigated in the resultant electrolyte solutions with Li| LiNi_0.8Co_0.1Mn_0.1O₂ half cells. The cells were cycled galvanostatically at 0.1 C (1 C=275 mAh g^-1) between 3.0 and 4.3 V at 30^oC. In 2.50 mol kg^-1 LiBF₄/PC+HFE (2:1 by vol., PC/Li⁺=2.39), the discharge capacity significantly decreased in 50 charge/discharge cycles. On the other hand, in 4.00 mol kg^-1 LiBF₄/PC+DMC+HFE (1:3:2 by vol., (PC+DMC)/Li⁺=1.58), 96.5% of the initial discharge capacity (193 mAh g^-1) was maintained even at the 50th cycle. The average Coulombic efficiency in the 50 cycles was also high at 99.7 %. Thus, the introduction of DMC into the PC+HFE system improved the charge/discharge cycle performance of LiNi_0.8Co_0.1Mn_0.1O₂ positive electrodes.