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1 M solutions of NaClO4 mixed with ethylene carbonate, dimethyl carbonate, and fluoroethylene carbonate were studied as electrolytes for a double-layer supercapacitor with electrodes made of Norit DLC Supra 30 activated carbon. It was shown that the specific capacity of activated carbon depends on the electrolyte composition, range of cycling voltages, and current density. The maximum specific capacitance of 40 F g–1 was obtained in 1 M NaClO4 mixed with ethylene carbonate: dimethyl carbonate: fluoroethylene carbonate (4: 5: 1) at a current density of 36 mA g–1 in the range 10–2300 mV. The minimum specific capacitance was obtained under the same cycling conditions in the electrolyte with 1 M NaClO4 + ethylene carbonate: dimethyl carbonate (1: 1). The variation of the specific capacitance with the electrolyte composition and range of cycling voltages is accounted for by the existence of a pseudocapacitance caused by the occurrence of side processes on the surface of activated carbon. The impedance spectroscopy was used to find that the introduction of fluoroethylene carbonate into the electrolyte positively affects the charge-transfer resistance and favors an increase in the specific capacitance of activated carbon.