We report the study of recharging behavior of CNT cloth material, which allows a large-scale and relatively cheap fabrication, as well as rather simple electrode design. Oxidative chemical purification procedure is applied prior electrode preparation to decrease the content of iron, which served as the catalyst for CNT fabrication. We demonstrate that this procedure, as well as anodic oxidation, results in the increase of CNT specific capacity in both alkaline and acidic aqueous solutions. Recharging rate is less sensitive to oxidation and remains fast enough: at 1 V/s scan rate the capacities in both acidic and alkaline solutions are close to 25 F/g. These characteristics allow to consider CNT cloth as a future stable backbone for materials of aqueous supercapacitors.