We performed density functional calculations to investigate the electronic and magnetic properties of BN-substituted non-classical fullerenes. The substitutional structures, binding energies, energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), ionisation potentials, electron affinities, vibrational frequencies and nucleus-independent chemical shifts (NICS) were systematically investigated. The binding energies of the BN-substituted non-classical fullerenes were found to be slightly smaller than those obtained for pure non-classical fullerenes. While the reverse trend was observed for BN-substituted C$_{46}$ and C$_{32}$ fullerenes, it was found that the BN-substituted C$_{62}$ fullerene has bigger ionisation potentials (IP) and smaller electron affinities (EA) than that of their parents. Because of low concentration of BN impurity, the IR spectra in the BN-substituted fullerenes are very similar to those of their parents, which can be considered as two separate regions: a low-frequency region at 200–1000 cm$^{−1}$ corresponding to the out-of-plane bending and breathing modes and a high-frequency region at 1000–1800 cm$^{−1}$ derived from the stretching of C–B, C–N, B–N and C–C bonds. It was shown that diatropic and paratropic ring currents of hexagons and pentagons together with the harshly antiaromatic character of the four-membered ring combine to produce a relatively small NICS at the centre of the C$_{62}$ and C$_{46}$ fullerene cages. The decrease in the antiaromatic and aromatic character of the B$_{2}$N$_{2}$ ring and the adjacent hexagons affects the aromaticity character of the BN-substituted fullerenes.