The rigid-rod polymer poly(1,5-naphthalenebenzobisthiazole) (Naph-1,5-PBT) was synthesized and spun into fibers from the lyotropic mesophase of the polymer in polyphosphoric acid by a dry-jet wet spinning method. The crystal structure of naph-1,5-PBT fibers was investigated using X-ray diffraction and molecular modeling methods. The 19 reflections, resolved from the X-ray pattern of the annealed Naph-1,5-PBT fiber, indicate that Naph-1,5-PBT has a perfect crystal structure without axial disorder, unlike other rigid-rod polymers such as poly(p-phenylenebenzobisthiazole) (PBT) and poly(p-phenylenebenzobisoxazole) (PBO). The observed reflections can be indexed with the triclinic unit cell parameters of a = 7.31 Angstrom, b = 3.68 Angstrom, c 12.68 Angstrom, and beta = 115.1degrees with the space group of PI, which one monomeric unit is. The torsion angle phi = 138degrees, at which the naphthalene unit is rotated toward the heterocyclic nitrogen atom, is derived from ab initio energy calculations as well as from the LALS refinement. The LALS refinement shows that the naphthalene ring is rotated by 4.4 +/- 4.6degrees from the ac plane on the projection along the c axis, and the chains are staggered side-by-side by c/4 in a regular way in the ac plane. The kinked structure, arising due to the naphthalene unit, as well as the twist structure introduced by the steric interaction between the naphthalene and heterocyclic rings, prevents axial disorders in the crystal which are usually observed in the rigid-rod polymers.