Hybrid supercapacitors, which combine a capacitive negative electrode and a faradaic positive electrode operating in an aqueous media, have many potential applications such as frequency regulation on the electrical grid, in particular when used in conjunction with intermittent energy sources. The purpose of this work is to study alternative designs to the aforementioned hybrid devices, by using composite materials which combine faradaic and capacitive contributions in the same electrode in order to maximize both energy and power densities. Cu2O:graphene composite materials have been synthesized using a simple precipitation technique in order to improve the energy of capacitive graphene-based negative electrode materials. Cuprous oxide (Cu2O) has been chosen due to its high theoretical capacity of 375 mAh.g−1 associated with an active electrochemical window in the range −0.85 V to −0.20 V vs Hg/HgO (1 M KOH), thus being a potential candidate to serve as a negative electrode to combine with the known carbon/Ni(OH)2 positive electrode in internal hybridized cell. An interesting initial capacity of more than 275 mAh g−1 has been obtained for the Cu2O:graphene composite material when cycled in a 6 M KOH solution at 0.1 mV s−1, despite a progressive fading of the specific capacity upon cycling.