In this work, the morphology of ZnO nanostructures is engineered to demonstrate enhanced supercapacitor characteristics of ZnO nanocones (NCs) compared to ZnO nanowires (NWs). ZnO NCs are obtained by chemically etching ZnO NWs. Electrochemical characteristics of ZnO NCs and NWs are extensively investigated to demonstrate morphology dependent capacitive performance of one dimensional ZnO nanostructures. Cyclic voltammetry measurements on these two kinds of electrodes in a three-electrode cell confirms that ZnO NCs exhibit a high specific capacitance of 378.5 F g-1 at a scan rate of 20 mV s-1, which is almost twice that of ZnO NWs (191.5 F g-1). The charge-discharge and electrochemical impedance spectroscopy measurements also clearly result in enhanced capacitive performance of NCs as evidenced by higher specific capacitances and lower internal resistance. Asymmetric supercapacitors are fabricated using activated carbon (AC) as the negative electrode and ZnO NWs and NCs as positive electrodes. The ZnO NC⫽AC can deliver a maximum specific capacitance of 126 F g-1 at a current density of 1.33 A g-1 with an energy density of 25.2 W h kg-1 at the power density of 896.44 W kg-1. In contrast, ZnO NW⫽AC displays 63% of the capacitance obtained from the ZnO NC⫽AC supercapacitor. The enhanced performance of NCs is attributed to the higher surface area of ZnO nanostructures after the morphology is altered from NWs to NCs.