This study reports the electrochemical performance of pseudosupercapacitor electrodes composed of cubic phase Co3O4 nanoparticles, reduced graphene oxide (rGO) and functionalized MWCNTs based nanocomposites. The Co3O4/rGO/CNTs nanocomposites have been synthesized using a hydrothermal method and the EPD technique has been used to make binder free electrodes of the nanocomposite materials for supercapacitor applications. The effects of graphene oxide (GO) concentration and the ratio of GO/CNTs on the electrochemical performance of the nanocomposite material have been investigated. From the experimental results, the Co3O4/rGO/CNTs nanocomposite synthesized with 2 mg mL-1 GO concentration and 10:1 GO/CNT ratio exhibits a good specific capacitance of 850 F g-1 at a 5 mV s-1 scan rate and 790 F g-1 at 1 A g-1, excellent rate capability and good cyclability in 1 M KOH. Furthermore, we have successfully designed an aqueous electrolyte-based asymmetric pseudocapacitor using Co3O4/rGO/CNTs nanocomposite as an anode and N-doped graphene nanocomposite as a cathode. The operating voltage of our optimized asymmetric pseudocapacitor is 1.4 V and it exhibits the maximum energy density and power density of 19.6 W h kg-1 and 7250 W kg-1, respectively. These results suggest that our EPD grown nanocomposite binder free electrode and our designed asymmetric pseudocapacitor have a good potential for practical applications.