Abstract: In order to prepare mimetic enzyme with hydrogen peroxide catalytic activity, CeO₂ was used as the research object in this paper, and nano-sized CeO₂ particles with peroxidase activity were prepared by hydrothermal method. The effect of preparation conditions of hydrothermal synthesis on catalytic performance of nano-sized CeO₂ for hydrogen peroxide was studied by the color reaction of Tetramethylbenzidine (TMB), including solid-liquid ratio, reaction temperature and reaction time. A nano-sized CeO₂ with the best catalytic activity was selected. Its structure was characterized and its steady-state kinetics of catalytic reaction was studied. The results showed that when the ratio of solid to liquid was 1:60 g/mL, the reaction temperature was 80 ℃ and the reaction time was 8 h, the absorbance value was the largest, which was 0.501, and the catalytic performance of nano-sized CeO₂ prepared by hydrothermal method was the best. The nano-sized CeO₂ crystals synthesized possessed fluorite structure. The catalytic reaction was in good agreement with the Michaelis-Menten equation, and the K_m value for H₂O₂ was 0.021 mmol/L. The results demonstrated that CeO₂ synthesized under simple reaction conditions in excellent purity showed high performance catalysts for H₂O₂.