Ab initio restricted Hartree-Fock method within the framework of large unit cell formalism is used to investigate the band structure of AlSb nanoclusters. Large unit cells of 8, 16, 54, 64 and 128 atoms are used to analyze the cohesive energy, energy gap, valence bandwidth, and the density of states of the energy levels for AlSb nanoclusters. The results of the present work revealed that the band structure of AlSb nanoclusters differs significantly from that of the bulk AlSb crystal. Also, it is found that the valence band width and the cohesive energy (absolute value) increase as the AlSb crystal size increases, and they tend to stabilize for nanoclusters of more than 50 atoms.