The application of the reported armchair transition-metal dichalcogenide (MoS2, MoTe2, MoSTe and WS2, etc.) nanotube is hindered for the optoelectronic devices due to the indirect band gap. By using first-principles calculations, the electronic structures of MoS2-xSex single-wall armchair nanotubes with respect to different diameters are investigated. The MoS2 armchair nanotube exhibits an indirect band gap as a function of nanotube diameters from 10 Å to 50 Å, whereas MoSSe and MoSe2 exhibit a surprising diameter-induced indirect-direct band gap crossover at the diameters of 25 Å and 33 Å, respectively. We also find that the optical properties of MoS2-xSex armchair nanotubes are anisotropic and strongly depend on the diameter.