A carbon nanotubes (CNTs)-nickel–cobalt hydroxide nanoflake core–shell structure is designed and fabricated by a facile one-step chemical bath deposition method. Structure analysis confirms that the as-synthesized hydroxides are conformally coated on the surface of CNTs with a hydrotalcite structure. The incorporation of Co into nickel hydroxides can improve the electrical conductivity together with intercalated sulphate ions into the interlayer spacing to enlarge the lattice space, which further improves the rate capabilities and cycling stability. Electrochemical data demonstrates that the hybrid hydroxide with Ni–Co molar ratio of 1:2 exhibits a high specific capacitance of 1151 F g−1 at 1 A g−1 and an excellent high rate capability, with 61% retention after a 70-fold increase in current densities. Its specific capacitance can maintain 77% of the initial value after 10,000 cycles. The nickel–cobalt hydroxide nanoflakes-CNTs hybrid shows a great potential of being an electrode material for supercapacitors with its high specific capacitance, good rate capability and long-term cycling life.