A new method based on one-step solvothermal reaction is demonstrated to synthesize ultrathin Ni–Co layered double hydroxide (LDH) nanosheets, which grow directly on a flexible carbon fiber cloth (NiCo-LDH/CFC). Through using 2-methylimidazole as complex and methanol as solvent, the as-prepared NiCo-LDH/CFC shows a (003) facet preferential growth and an expanded interlayer spacing structure, resulting in a unique 3D porous nanostructure with a thickness of nanosheets of around 5–7 nm that shows high energy storage performance. By controlling the ratio of Ni/Co = 4:1 in the precursor solution, the electrode shows a specific capacitance of 2762.7 F g^–1 (1243.2 C g^–1) at a current density of 1 A g^–1. Nevertheless, the optimal composition is obtained with Ni/Co = 1:1, which produces a specific capacitance of 2242.9 F g^–1 (1009.3 C g^–1) at 1 A g^–1 and shows an excellent rate capability with 61% of the original capacitance being retained at a current density of 60 A g^–1. The hybrid supercapacitor (HSC) based on the NiCo-LDH/CFC exhibits a maximum energy density of 59.2 Wh kg^–1 and power densities of 34 kW kg^–1, respectively. Long-term stability test shows that 82% of the original capacitance of the HSC remains after 5000 cycles. Importantly, the electrochemical performance of the solid-state flexible supercapacitors based on the prepared NiCo-LDH/CFC electrode showed a negligible change when the device was bent up to 180°. The performance of synthesized NiCo-LDH/CFC indicates the great potential of the material for delivering both high energy density and high power density in energy storage devices.