To enable next-generation high-energy-density lithium (Li)-metal batteries (LMBs), an electrolyte that has simultaneous high Li-metal Coulombic efficiency (CE) and high anodic stability on cathodes is of significant importance. Sulfones are known for strong resistance against oxidation, yet their application in LMBs is restricted because of their poor compatibility with Li-metal anodes, high viscosity, and poor wettability. Here, we demonstrate that a high Li CE over 98% can be achieved in concentrated sulfone-based electrolytes. Furthermore, the viscosity and wettability issues of sulfones are resolved by the addition of a fluorinated ether, 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether, to form a localized high-concentration electrolyte (LHCE), which not only provides further improvement in Li CE (98.8%) but also remains anodically stable with high-voltage cathodes, suppresses Al corrosion, and enables LMBs to operate in a wide temperature range. As a result, significantly improved cycling performance of LMBs has been realized with sulfone-based LHCE. For high-voltage rechargeable lithium (Li)-metal batteries (LMBs), electrolytes with good stabilities on both the highly oxidative cathodes and the highly reductive Li-metal anodes are urgently desired. Sulfones have excellent oxidative stability, yet their high viscosity, poor wettability, and, in particular, incompatibility with Li anodes greatly hinder their applications in LMBs. Here, we demonstrate that a high Li Coulombic efficiency (CE) of 98.2% during repeated Li plating and stripping cycles can be realized in concentrated lithium bis(fluorosulfonyl)imide (LiFSI)-tetramethylene sulfone electrolyte. More importantly, the localized high-concentration electrolyte, formed by the dilution of the high-concentration electrolyte with a non-solvating fluorinated ether, 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether, solves the viscosity and wettability issues, further improves Li CE (98.8%), and improves the high-voltage (4.9 V) performance of LMBs with effective Al protection. High-voltage batteries with Li-metal anodes can offer desirable high energy densities. Despite their excellent oxidative stability, sulfones have various limitations to be useful in Li-metal batteries, in particular their instability with Li metal. Here, we achieved a high Li Coulombic efficiency of nearly 99% in a sulfone-based localized high-concentration electrolyte (LHCE) with the addition of a non-solvating co-solvent. In addition, this co-solvent is highly beneficial for realizing stable battery cycling up to 4.9 V.