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Solid-state electrolytes in rechargeable all-solid-state Li-metal batteries,which have better safety and higher specific capacity than conventional rechargeable Liion batteries with liquid electrolytes,are limited by the low Li-ion conductivity of the solid electrolyte and the large electrolyte/electrode interfacial resistance.Here,we report a new rhombohedral NASICON structure Li1.4Sr0.2Hf1.8(PO4)3 with a high Li-ion conductivity of 1.62 × 10-5 S·cm-1 at 25 ℃,and its conductivity can be improved to 3.4 × 10-5 S·cm-1 after the densification of the pellet by hot pressing.Li1.4Sr0.2Hf1.8(PO4)3 coated by a thin layer of polymer electrolyte showed a stable lowimpedance dendrite-free plating/stripping process in a symmetric Li/Li cell for 100 h;moreover,the Li1.4Sr0.2Hf1.8(PO4)3 electrolyte had a small interfacial resistance in all-solid-state Li/LiFePO4 cell,which allows a high Coulombic efficiency and good cycling of the cell.