Solid-state sodium batteries (SSSBs) display great potential in scale energy storage for their safety, cost and sustainability. However, it is a great challenge to achieve high ionic conductivity and temperature adaptability for most sodium-ion solid electrolytes. Here, we first demonstrate that Sc3+-doped Na3Zr2Si2PO12 (NASICON) is a promising electrolyte for a wide temperature range utilizing in SSSBs from 0 to 80 °C. Optimal Na3.4Zr1.6Sc0.4Si2PO12 shows a superior Na-ion conductivity, up to 1.77 × 10−3 S cm−1 at room temperature, and excellent Na metal compatibility, as confirmed by a symmetrical cell test. Furthermore, the solid-state sodium battery with the configuration of Na3V2(PO4)3/Na3.4Zr1.6Sc0.4Si2PO12/Na maintains a discharge capacity of 98.7 mAh g−1 at 1C after 300 cycles at room temperature. Even at 0 °C, the battery still displays a reversible capacity of 99.2 mAh g−1 at 0.1C after 100 cycles. Through the structure analysis and ex-situ and in-situ electrochemical characterizations, the reasons that dominate the excellent performance of the assembled all-solid-state sodium battery with NASICON electrolytes are initially revealed.