As a potential solution to ubiquitous energy concerns, anion-exchange membranes (AEMs) have been widely used as the electrolyte in alkaline fuel cells (AFCs), and significant refinement of AEMs has been achieved in the past few decades. However, it remains unknown whether AEMs can be used as an electrolyte in a solid-state supercapacitor or zinc–air battery. A low-cost alkaline exchange membrane electrolyte composed of chitosan and poly(diallyldimethylammonium chloride) that possesses a high OH– conductivity (0.024 S cm–1), strong alkaline stability (216 h at 8 M KOH), good thermal stability, and low degree of anisotropic swelling, was found to provide a high electrochemical performance in all-solid-state devices. Prototypes of the solid AFC with the membrane shows superior stability over 500 h. The carbon nanotube-based all-solid-state supercapacitor with the membrane generated a rectangular cyclic voltammetry curve up to 10 V s–1 and excellent cycling stability of 4000 cycles with 84% specific capacitance retention. The all-solid-state zinc–air battery demonstrates high power density (48.9 mW cm–2). These advantages indicate that the membrane is a promising electrolyte for all-solid-state electrochemical devices.