For renewable energy sources such as solar, wind, and hydroelectric to be effectively used in the grid of the future, flexible and scalable energy-storage solutions are necessary to mitigate output fluctuations(1). Redox-flow batteries (RFBs) were first built in the 1940s(2) and are considered a promising large-scale energy-storage technology(1,3,4). A limited number of redox-active materials(4,5-10)-mainly metal salts, corrosive halogens, and low-molar-mass organic compounds have been investigated as active materials, and only a few membrane materials(3,5,11-14), such as Nafion, have been considered for RFBs. However, for systems that are intended for both domestic and large-scale use, safety and cost must be taken into account as well as energy density and capacity, particularly regarding long-term access to metal resources, which places limits on the lithium-ion-based and vanadium-based RFB development(15,16). Here we describe an affordable, safe, and scalable battery system, which uses organic polymers as the charge-storage material in combination with inexpensive dialysis membranes, which separate the anode and the cathode by the retention of the non-metallic, active (macro-molecular) species, and an aqueous sodium chloride solution as the electrolyte. This water- and polymer-based RFB has an energy density of 10 watt hours per litre, current densities of up to 100 milliamperes per square centimetre, and stable long-term cycling capability. The polymer-based RFB we present uses an environmentally benign sodium chloride solution and cheap, commercially available filter membranes instead of highly corrosive acid electrolytes and expensive membrane materials.