With the purpose of the enhancement of supercapacitor behaviour, a CuZnAl-layered double hydroxide/ graphene (CuZnAl-LDH/GO) nanohybrid was synthesized via facile method. The layered structures of GO and CuZnAl-LDH lead to create favourable conditions for energy storage capacity. The prepared CuZnAl/GO nanohybrid was characterized by X-ray diffraction, inductively coupled plasma optical emission spectrometry analysis, field-emissionscanning electron microscopy and energy dispersive X-ray spectroscopy, N$_2$ adsorption/desorption analysis measurements. The electrochemical behaviour of prepared nanohybrid was evaluated by conventional cyclic voltammetry, galvanostatic charge–discharge and electrochemical impedance spectroscopy techniques. As a supercapacitor, the prepared CuZnAl/GO nanohybrid electrode revealed higher specific capacitance (3.87 F cm$^{-2}$) than CuZnAl-LDHs (1.37 F cm$^{-2}$). The CuZnAl/GO nanohybrid exhibited good stability, with high specific capacitance for over 1000 charge–discharge cycles. The obtained results can be justified by enhancing electrochemically active areas provided by layered structures of LDH and preventing effect of GO in the aggregation of LDH sheets. Moreover, the GO increase the electrical conductivity in nanohybrid. The facile synthesis and high electrochemical performance of CuZnAl/GO nanohybrid showed that this hybrid material can be suitable as an electrode material for energy storage and supercapacitor devices.