Common battery electrolytes comprise organic carbonate solvents and fluorinated salts based on hexafluorophosphate (PF6–) anions. However, these electrolytes suffer from high flammability, limited operating temperature window, and high cost. To address those issues, we here propose a fluorine-free electrolyte based on sodium bis(oxalate)borate (NaBOB). Although lithium bis(oxalate)borate (LiBOB) has previously been investigated for lithium-ion batteries, NaBOB was considered too insoluble in organic solvents to be used in practice. Here, we show that NaBOB can be dissolved in mixtures of N-methyl-2-pyrrolidone (NMP) and trimethyl phosphate (TMP) and in each sole solvent. NMP provides higher solubility of NaBOB with a concentration of almost 0.7 M, resulting in an ionic conductivity up to 8.83 mS cm–1 at room temperature. The physical and electrochemical properties of electrolytes based on NaBOB salt dissolved in NMP and TMP solvents and their binary mixtures are here investigated. The results include the thermal behavior of the sole solvents and their mixtures, flammability tests, NaBOB solubility, and ionic conductivity measurements of the electrolyte mixtures. Full-cell sodium-ion batteries based on hard carbon anodes and Prussian white cathodes were evaluated at room temperature and 55 °C using the aforementioned electrolytes. The results show a much improved performance compared to conventional electrolytes of 1 M NaPF6 in carbonate solvents at high currents and elevated temperatures. The proposed electrolytes provide a high ionic conductivity at a wide temperature range from room temperature to −60 °C as NMP–TMP mixtures have low freezing points. The flammability tests indicate that NaBOB in NMP–TMP electrolytes are nonflammable when the electrolyte contains more than 30 vol % TMP.