Magnetite and inorganic sludge were mainly composed of $Fe_2O_4$ and $Fe_2O_3$, respectively. Initial specific surface areas of magnetite and inorganic sludge were 130 $m^2$/g and 31.7 $m^2$/g. $CO_2$ decomposition rate for inorganic sludge was increased with temperature. Maximum $CO_2$ decomposition rates were shown 89% for magnetite at $350^{circ}C$ and 84% for inorganic sludge at $500^{circ}C$. Specific surface area for magnetite was not varied significantly after $CO_2$ decomposition. However, specific surface area for inorganic sludge was greatly decreased from initial 130 $m^2$/g to approximately 50~60 $m^2$/g after reaction. Therefore, it was estimated that magnetite could be used for $CO_2$decomposition for a long time and inorganic sludge should be wasted after $CO_2$ decomposition reaction.