A carbon nanotubes (CNTs)-nickel-cobalt oxyhydroxide nanoflake core-shell structure is designed and fabricated by a facile one-step chemical bath deposition method at 80°C. After its annealing at 300°C, a CNTs/Ni-Co oxide core-shell heterostructure is thus achieved. Phase characterization proves that Ni-Co oxyhydroxide and Ni-Co oxide as shells are (Ni,Co)OOH and NiCo2O4, respectively. Structural analysis confirms that the as-synthesized oxyhydroxide and oxide shells are conformally coated on the external surface of CNTs. Electrochemical data demonstrate that (Ni,Co)OOH/CNTs composite exhibits a high specific capacitance of 853Fg−1 at 5mVs−1 and an excellent high rate capability, with 75% retention after a 10-fold increase in current density. Meanwhile, the hybrid of NiCo2O4/CNTs has an enhanced performance of 940Fg−1 at 5mVs−1. Its rate capability is much better than the oxyhydroxide precursor because of its high conductivity. Both of these heterostructures have an excellent cycling performance of 100% capacitance retention after 10,000 cycles and Coulombic efficiency. An asymmetric capacitor is also fabricated with (Ni,Co)OOH/CNTs as positive electrode and activated carbon as negative electrode. It possesses a high specific capacitance of 164Fg−1 and a high energy density of 73.8WhKg−1 within 1.8V.