The invention relates to a copper-iron layered double metal hydroxide, a copper-iron layered double metal hydroxide/carbon based composite material as well as preparation methods and application of the copper-iron layered double metal hydroxide and the composite material. The preparation method of the copper-iron layered double metal hydroxide includes the following steps: (1) dissolving a metal copper salt and a metal iron salt into deionized water to obtain a mixed solution; and (2) adding an alkaline reagent into the mixed solution, adjusting the pH to 5-7, and performing aging at 60-130 DEG C for 20-80 h to obtain the copper-iron layered double metal hydroxide.