Potassium-ion batteries are an emerging post-lithium technology that are considered ecologically and economically benign in terms of raw materials’ abundance and cost. Conventional cell configurations employ flammable liquid electrolytes that impose safety concerns, as well as considerable degrees of irreversible side reactions at the reactive electrode interfaces (especially against potassium metal), resulting in a rapid capacity fade. While being inherently safer, solid polymer electrolytes may present a solution to capacity losses owing to their broad electrochemical stability window. Herein, we present for the first time a stable solid-state potassium battery composed of a potassium metal negative electrode, a Prussian blue analogue K₂Fe[Fe(CN)₆] positive electrode, and a poly(ethylene oxide)-potassium bis(trifluoromethanesulfonyl)imide polymer electrolyte. At an elevated operating temperature of 55 °C, the solid-state battery achieved a superior capacity retention of 90% over 50 cycles in direct comparison to a conventional carbonate-based liquid electrolyte operated at ambient temperature with a capacity retention of only 66% over the same cycle number interval.