The spinel $LiMn_{2}O_{4}$ powders were synthesized at $480^{circ}C$ for 12 h in air by a sol-gel method using manganese acetate and lithium hydroxide as starting material and the $Fe_{3}O_{4}$ powders were synthesized by the precipitation method using $0.2M-FeSO_{4}{cdot}H_{2}O$ and 0.5M-NaOH. The synthesized $Fe_{3}O_{4}$ powders were mixed at portion of 5, 10, 15 and 20 wt% about $LiMn_{2}O_{4}$ powders through ball-milling followed by drying at room temperature for 48 h in air. The mixed catalysts were reduced at $350^{circ}C$ for 3 h by hydrogen and the decomposition rate of carbon dioxide was measured at $350^{circ}C$ using the reduced catalysts. As the results of $CO_{2}$ decomposition experiments, the decomposition rates of carbon dioxide were 85% in all catalysts but the initial decomposition rates of $CO_{2}$ were slightly high in the case of the $5%-Fe_{3}O_{4}$ added catalyst.