An all-solid-state hybrid supercapacitor/rechargeable battery with RbAg₄I₅ superionic ceramic electrolyte was fabricated without air-proof sealing. The ionic conductivity of RbAg₄I₅ powders was 0.21 S cm^-1. The all-solid-state SC/battery can work in oxygen and moisture environment at room temperature. The all-solid-state energy storage device shows both SC-like and battery-like behaviors. The maximum specific energy of the all-solid-state SC was more than 60 Wh kg^-1. The ESR of the all-solid-state SC increases with charge/discharge cycles. The charge capacity first increases and then decreases with charge/discharge cycles. However, the charge capacity can be recovered by conducting an annealing process at 150°C for 12 hours. The possible reason is that Rb₂AgI₃ and AgI produced in charge/discharge cycles are converted back to RbAg₄I₅ in the annealing process. X-ray diffraction analyses were conducted before and after a number of charge/discharge cycles and before and after the annealing process. It was also found that air and or moisture were necessary for the electrochemical charge/discharge processes. Systematic heat treatments and electrochemical measurements were conducted to specify the optimal operational parameters and for elucidating the charge/discharge mechanisms of the hybrid supercapacitor/battery. The experimental results indicate that the main charge/discharge mechanism is redox reactions of the electrolyte and little electrode material is consumed. Thus, the electrodes can be made very thin to reduce the total mass and increase the specific energy and power.