The nanostructured cobalt hydroxide [Co(OH)2] embedded carbon nanotubes (CNT) have been synthesised by a simple chemical reflux method. The crystallinity of cobalt hydroxide has been confirmed by using powder X-ray diffraction data. The presence of CNT in the synthesised nanocomposite is also examined. Fourier transform infrared spectroscopy reveals the OH and CoO vibrations in the Co(OH)2/fCNT nanocomposite. SEM and TEM images expose the surface morphology of Co(OH)2 sheet that is embedded over carbon nanotube. The electrochemical performance of the Co(OH)2 embedded fCNT has been examined by the cyclic voltammetry in 6 M potassium hydroxide (KOH) electrolyte in room temperature. Co(OH)2 embedded fCNT nanocomposite exhibits higher specific capacitance up to 1006.8 F/g at 0.5 mV s−1 scan rate. The specific capacitance of Co(OH)2 embedded fCNT nanocomposite is calculated from the charge-discharge curve. The synthesised hybrid nanocomposite is used as a cathode, and the functionalized CNT is used as an anode. These are used to fabricate an asymmetrical supercapacitor device. The device is delivered to a high power density of 7000 W kg−1 and energy density of 17 W h kg−1 in the potential window from 0 V to 1.4 V. The results of hybrid Co(OH)2/fCNT||fCNT asymmetrical supercapacitor exhibit better cycle stability up to 5000 cycles. The usefulness of Co(OH)2/fCNT||fCNT asymmetrical supercapacitor is analysed for energy storage devices.