The demand of sustainable power supply requires high-performance cost-effective energy storage technologies. Here we report a high-rate long-life low-cost sodium-ion battery full-cell system by innovating both the anode and the electrolyte. The redox couple of manganese(I/II) in Prussian blue analogs enables a high-rate and stable anode. Soft X-ray absorption spectroscopy and resonant inelastic X-ray scattering provide direct evidence suggesting the existence of monovalent manganese in the charged anode. There is a strong hybridization between cyano ligands and manganese-3d states, which benefits the electronic property for improving rate performance. Additionally, we employ an organic-aqueous cosolvent electrolyte to solve the long-standing solubility issue of Prussian blue analogs. A full-cell sodium-ion battery with low-cost Prussian blue analogs in both electrodes and co-solvent electrolyte retains 95% of its initial discharge capacity after 1000 cycles at 1C and 95% depth of discharge. The revealed manganese(I/II) redox couple inspires conceptual innovations of batteries based on atypical oxidation states.