Covalent functionalization of a $Zn_{12}O_{12}$ nano-cage with $CO_2$ molecule in terms of energetic, geometry, and electronic properties was investigated by density functional theory method. For chemisorption configurations, the adsorption energy of $CO_2$ on the $Zn_{12}O_{12}$ nano-cage for the first $CO_2$ was calculated -1.25 eV with a charge transfer of 1.00|e| from the nano-cage to the $CO_2$ molecule. The results show that $CO_2$ molecule was significantly detected by pristine $Zn_{12}O_{12}$ nano-cage, therefore the nano-cage can be used as $CO_2$ storage. Also, more efficient binding could not be achieved by increasing the $CO_2$ concentration. For Physisorption configurations, HOMO-LUMO gap of the configurations has not changed, while slight changes have been observed in the chemisorption configurations.