The excited states of a series of semiconducting zigzag (n, 0) tubes are studied using the GW method and the Bethe-Salpeter equation within the ab initio many-body perturbation theory. The optical variation rule of the excitation energy with the tube diameter exhibits a family pattern, which arises from the electronic structure of the pristine tube and depends on the value of n mod 3. The introduction of single vacancy and Stone-Wales defects with different orientations affords an effective route for modulating the band structures and optical spectra, resulting in the variation of the selection rules of the excitons and turning dipole-forbidden excitons into dipole-allowed ones. The new localized impurity states in defected tubes will provide additional optically allowed transitions and give rise to pronounced satellite red-shifted peaks. These findings provide inspiration for the tune of optical properties of carbon nanotubes in the future for applications in optoelectronics.