Carbon nanotubes are widely employed as catalyst supports and electrode materials. In our earlier studies, capacitance characteristics of carbon nanotubes (CNTs) and nitrogen-doped carbon nanotubes (N-CNTs) were measured. Voltammetric curves obtained for nitrogen-doped nanotubes in an acid electrolyte showed pseudocapacitance peaks that were caused by electrochemical processes involving nitrogen-containing functional groups. In this study, measurements were made in a two-electrode cell of a supercapacitor with a hydrophilic polypropylene PORP-A1 film serving as a separator in alkaline (6 M KOH solution) and acid (1 M H2SO4 solution) electrolytes using a PARSTAT 4000 potentiostat/galvanostat. A technique was developed to estimate the contribution of electrical double layer (EDL) by subtracting pseudocapacitance from total capacitance of a cell using the Origin 9 software. The contribution of EDL and pseudocapacitance to the capacitance of supercapacitor cells was estimated. The highest capacitance of an electrode material equal to 97.2 F/g (including the EDL capacitance of 65 F/g) was reached for nanotubes doped with 8.5% of nitrogen in an acid electrolyte at a potential scanning rate of 10 mV/s.