A highly flexible yet high‐energy‐density cathode for lithium‐ion batteries is fabricated with a novel redox‐active binder polymer composed of 2,2,6,6‐tetramethylpiperidine 1‐oxyl (TEMPO) with vinyl ether main chain, lithium cobalt oxide, and single‐walled carbon nanotube. The cathode itself and its battery display excellent durability against repeated bending over 104 times. The highest volumetric capacity beyond 300 mAh cm−3 as a flexible electrode is achieved based on the highly adhesive and redox‐active, robust radical polyether binder. A highly flexible, only 0.5 mm‐thick, lithium‐ion battery charge/discharges repeatedly with constant output around 3.8 V even under rapid bending. Herein, the operation of flexible electronic devices with well‐balanced energy density and power‐supplying purposes is discussed.