Specific energy and self-discharge are two important performances of electrochemical capacitors. In this work, we have fabricated the composite electrodes by complexing the negatively charged carboxylated multi-walled carbon nanotubes (cMWCNT) with the redox active units-containing positively charged random copolymers. 2,2,6,6-Tetramethylpiperidinyl-N-oxyl and viologen are employed as model redox active units to exemplify the strategy of the concurrent increase of specific energy and suppression of self-discharge of a two-electrode device. The enhanced specific energy is mainly attributed to the increased electrolyte decomposition window induced by the faster redox reactions than those of the hydrogen and oxygen evolution reactions. The improved performance of self-discharge is due to the suppression of the cross-diffusion and redox shuttling of the redox couples induced by the complexation between the cMWCNT and the copolymers. By employing the redox active units-containing charged copolymers, this work provides a convenient and universal strategy to concurrently increase specific energy and suppress self-discharge of electrochemical capacitors with the carbon-based electrodes.