The influence of pretreatment of multiwalled carbon nanotubes (MWCNTs) in oxidizers (solutions of H2O2 and HNO3) on the structure and electrochemical properties of composites with layered potassium-manganese oxide (KxMnO2) was studied. Composites were obtained by soaking carbon nanotubes in an aqueous solution of KMnO4 at 60 °C. The electrochemical performance of the composites was evaluated by cyclic voltammetry and galvanostatic charge‒discharge methods. It has been established that stronger oxidation of the MWCNTs surface at the functionalization stage leads to a noticeable increase in the reaction rate as well as the optimal potassium content in the KxMnO2 composition, which provides higher capacitive characteristics of the composite (a maximum specific capacitance of 150 F g−1 and a rate capability of 43% with increasing density current from 0.1 to 2.0 A g−1). The resulting composites are promising active components for increasing the capacitive characteristics of conductive carbon black (CB). Compared with an electrode based only on CB, electrodes based on a combination of the composite and CB at a mass ratio of 1:1 showed specific capacitance values approximately 1.5 to 3 times greater, as well as a twofold increase in rate capability (from 35 to 70%) in the range of discharge current density 0.1 to 2.0 A g−1.