Transition metal oxides have a higher theoretical capacity as anode materials for lithium-ion batteries (LIBs). However, they often suffer from poor capacity retention owing to their low electrical conductivity and large volume variations during the charge/discharge process. Carbon coating is an effective way to enhance the electrical conductivity of metal oxides. The synergistic effects of the two components can also effectively improve the electrochemical performance of the material. In this study, MnO$_{2}$@ZIF-67 organic-inorganic hybrid nanostructures were prepared using MnO$_{2}$ nanowires as a template. N-doped carbon-coated MnO@CoMn$_{2}$O$_{4}$ nanowire composites (MnO@CoMn$_{2}$O$_{4}$@N-C) were synthesised by annealing. The organic ligand of ZIF-67 underwent carbonisation during high-temperature calcination to produce N-doped carbon, which improved the electrical conductivity. When MnO@CoMn$_{2}$O$_{4}$/N-C nanowire composites were used as the anode material for LIBs, a discharge capacity of 1 594.6 mA$\cdot$h/g was achieved in the first cycle, with a retention capacity of 925.8 mA$\cdot$h/g even after 100 cycles at current density of 0.1 A/g and a reversible capacity of 837.6 mA$\cdot$h/g at 0.5 A/g. It also had an excellent rate cycling performance. The outstanding electrochemical performance was attributed to the unique structure as well as the coating effect of N-doped carbon.