Improvement in the capacitance and energy density of zinc cobalt oxides based materials is vital for creating supercapacitors with excellent electrochemical performance. We synthesised Cu doped Zinc Cobalt oxides (Zn1-xCuxCo2O4) nanostructures via a facile hydrothermal method to accomplish excellent supercapacitive performance. Significantly, the incorporation of Cu into ZnCo2O4 brings a 2 times increase in specific surface area (52 m2g-1) and decrease in charge transfer resistance for Zn0.7Cu0.3Co2O4 (x=0.3) sample. Consequently, Cu doped Zn0.7Cu0.3Co2O4 electrode displays high specific capacitance of 1425 Fg-1, which is 1.55-fold increased as compared to 917 Fg-1 of pristine ZnCo2O4 electrode. About 96 % of capacitance is retained by the Zn0.7Cu0.3Co2O4 after 2000 charge-discharge cycles. Later, Zn0.7Cu0.3Co2O4 based solid-state symmetric supercapacitor has been fabricated, which displays the potential window of 1.5 V with enlarged cycling stability. The assembled device shows high energy density of 55 Whkg-1 at a power density of 2621 WKg-1 and successfully lighten the yellow LED of 1.5 V. The immense improvement in electrochemical performance is credited to increased surface area and electronic conductivity of electrode. The obtained results clearly evidenced that fabricated solid-state symmetric supercapacitor has the potential to be used in flexible energy storage devices.