Strong binding of an isolated carbon dioxide molecule over three different aluminium nitride (AlN) nanostructures (nanocage, nanotube and nanosheet) is verified using density functional calculations. Equilibrium geometries, electronic properties, adsorption energies and thermodynamic stability of each adsorbed configuration are also identified. Optimized configurations are shown at least one corresponding physisorption and chemisorption of CO2 molecule over different AlN nanostructures. Also, the effect of chirality on the adsorption of CO2 molecule is studied over two different finite-sized zigzag (6,0) and armchair (4,4) AlN nanotubes. It is found that the electronic properties of the Al12N12 nanocage are more sensitive to the CO2 molecule than other AlN nanostructures. This indicates the significant potential of Al12N12 nanocage toward the CO2 adsorption, fixation and catalytic applications in contrast to other AlN nanostructures.