Energy storage devices, such as lithium-ion batteries and supercapacitors, are required for the modern electronics. However, the intrinsic characteristics of low power densities in batteries and low energy densities in supercapacitors have limited their applications. How to simultaneously realize high energy and power densities in one device remains a challenge. Herein a fiber-shaped hybrid energy-storage device (FESD) formed by twisting three carbon nanotube hybrid fibers demonstrates both high energy and power densities. For the FESD, the energy density (50 mWh cm−3 or 90 Wh kg−1) many times higher than for other forms of supercapacitors and approximately 3 times that of thin-film batteries; the power density (1 W cm−3 or 5970 W kg−1) is approximately 140 times of thin-film lithium-ion battery. The FESD is flexible, weaveable and wearable, which offers promising advantages in the modern electronics.