In the present study, nano-size powders of ternary ferrites, $Ni_{0.5}Zn_{0.5}Fe_2O_4$, as the potential catalysts of $CO_2$decomposition, were prepared by the wet processing of hydrothermal synthesis and coprecipitation method, and the catalyzing effects of impregnation of the noble metals, Pt and Pd, onto $Ni_{0.5}Zn_{0.5}Fe_2O_4$for the $CO_2$decomposition were investigated. XRD results of the synthesized ferrites showed a typical spinel structure of ferrite and the particle size was very small as about 6~10 nm. BET surface area of the ternary ferrites was not affected by the impregnation of Pt and Pd. The reactivity of the $CO_2$decomposition to carbon was improved by the impregnation of the noble metals of Pd and Pt. The effect of Pd-impregnation on the $CO_2$decomposition rate was higher than Pt-impregnation.