Copper–copper hydroxide-electrochemically reduced graphene oxide (Cu–Cu(OH)2/RGO) nanocomposite is formed successfully on stainless steel (SS) in two steps: (i) electrophoretic deposition of nanocomposite film from CuSO4 and graphene oxide (GO) colloidal suspension on SS and (ii) electrochemical reduction of prepared electrode in 0.5 M NaNO3 electrolyte. Cu–Cu(OH)2/RGO is characterized by X-ray diffraction, atomic force microscopy (AFM), field emission scanning electron microscopy (FESEM) and energy dispersive X-ray spectrometry. AFM and FESEM images indicate the homogenous distribution of Cu–Cu(OH)2 nanoparticles on the surface of RGO. The electrochemical properties of Cu–Cu(OH)2–RGO/SS are investigated by cyclic voltammetery, galvanostatic charge/discharge technique and electrochemical impedance spectroscopy. Cu–Cu(OH)2–RGO/SS exhibits a high capacitance of 333 F g−1 in 0.5 M Na2SO4 electrolyte which is two times higher than that of RGO/SS (192 F g−1) and indicate the positive effect of Cu–Cu(OH)2 on capacitance of electrode. Also, it is observed that with addition of 0.1 M Fe(CN)3−∕4−6 into aqueous solution of 0.5 M Na2SO4, the electrochemical performance of Cu–Cu(OH)2–RGO/SS increases substantially and shows a high specific capacitance of 492 F g−1 at current density of 5 A g−1, which is higher than that of Cu–Cu(OH)2–RGO/SS (333 F g−1). A positive effect of the presence of Fe(CN) 3−∕4− 6 in the electrolyte is due to electron relay of Fe(CN) −3 6 ∕Fe(CN) −4 6 ion pair at the electrode/electrolyte interface by coupling in the redox transition of Cu(I)/Cu(II). The electrochemical tests indicate that Cu(OH)2–RGO/SS in 0.5 M Na2SO4 electrolyte containing 0.1 M Fe(CN) 3−∕4− 6 shows an outstanding cyclic stability with specific retention of 97% after 500 cycles.