Carbon nanotubes, one of the most advanced nanoscale materials, have attracted much research attention since they exhibited semiconductor, metal or insulator properties depending on their geometric structures. Carbon nanotubes have great potential in various applications in electronic and optical device. Dopants to the carbon nanotubes intentionally could offer a possible route to change and tune their electronic, optical properties. Another important and effective method is to deform the carbon nanotubes structure. Superlattice structures can offer extra degrees of freedom in designing electronic, optical devices. To understand the involved mechanism, in this paper, the geometry structures, electronic structures and optical properties of the armchair carbon nanotube superlattices doped cyclic alternately with B and N under different shear deformations are investigated by the first-principles method through using the CASTEP code in MS 6.0. It is found that the structures of carbon nanotube superlattices can be dramatically changed by shear deformation. When the shear deformation is less than 9%, the optimization geometry structures of carbon nanotube superlattices are still similar to tubular structures, when the shear deformation is greater than 12%, the geometry structures of these systems have large distortions. The results about the binding energy show that the shear deformation changes the stability of the armchair doped carbon nanotube superlattice. The larger the shear deformation, the lower the stability of the doped carbon nanotube superlattices is. The analysis of charge population show that the covalent bond and ionic bond coexist in the armchair carbon nanotube superlattices doped cyclically alternately with B and N. The band gap of the carbon nanotube superlattice is affected by N, B dopants, as a result, the carbon nanotube superlattice changes from a metal to a semiconductor. Compared with the (5, 5) nanotube superlattices, the band gaps of the (7, 7), (9, 9) doped carbon nanotube superlattices increase. With increasing the shear deformation, the band gap of the doped carbon nanotube superlattices decreases gradually, when the shear deformation is greater than 12%, the band gap changes into 0 eV, the carbon nanotube superlattice changes back into a metal from a semiconductor. The analysis of density of states obtains the same conclusions as the energy band analysis. In optical properties, compared with the armchair carbon nanotube superlattices doped cyclically alternately with B and N without shear deformation, those systems under shear deformation have the peaks of the absorption coefficient and the reflectivity that are all reduced, and are all red-shifted.