Using density functional theory calculations, we investigated the adsorption of cyanogen chloride (ClCN) on the pristine and Al-doped BN nanocones, nanocages, and nanosheets. The order of magnitude of gap for the pristine BN structures is calculated to be as follows: cage > sheet > cone. The large interaction distances, small adsorption energies, and small charge transfers indicate that the interaction between the ClCN and pristine BN nanostructures is weak. The order of reactivity toward ClCN (R) is predicted to be as follows: R-cage > R-cone > > R-sheet. The ClCN cannot sensibly affect the highest and lowest occupied molecular orbitals (HOMO, LUMO), and gap of these BN nanostructures. The Al doping significantly increases the strength of the interaction because the Al atom is projected out of the wall of the BN nanostructures and becomes more accessible. Also, the energy of LUMO levels of the Al-doped BN nanostructures are more close to the energy of HOMO level of ClCN (similar to - 9.14 eV) compared to the LUMO of pristine BN structures. We found that after the ClCN molecule adsorption, the electrical conductivity of all Al doped BN nanostructures increases considerably which helps to detect this molecule. Our results suggest that Al-doped BN nanosheet is a better sensor compared to the Al-doped BN nanocone and nanocage because of its higher sensitivity (28.8% decrease in gap by ClCN adsorption) and shorter recovery time (0.02 s).