The spinel $Fe_{3}O_{4}$ powders were synthesized using 0.2 $M-FeSO_4{cdot}7H_{2}O$ and 0.5 M-NaOH by oxidation in air and 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 materials. The synthesized $LiMn_{2}O_{4}$ powders were mixed at portion of 5, 10, 15 and 20 wt% of $Fe_{3}O_{4}$ powders using a ball-mill. The mixed catalysts were dried at room temperature for 24 hrs. The mixed catalysts were reduced by hydrogen gas at 350 $^{circ}C$ for 2 h. The carbon dioxide decomposition rates of the mixed catalysts were 90% in all the mixed catalysts but the decomposition rate of carbon dioxide was increased with adding $LiMn_{2}O_{4}$ powders to $Fe_{3}O_{4}$ powders.