The electron excitations of Single-Walled Silicon Nanotubes (SWSiNTs), with sp(2) and sp(3) hybridization, were studied using the localized-density-matrix (LDM) method with INDO/S parameters. Strong anisotropic characteristics of the dynamic polarizabilities were found for all the nanotubes. The transitional intensity along the tubular axis is much larger than that perpendicular to the axis for all the nanotubes. The optical gaps of sp(3)-hybridized infinitely-long pentagonal SWSiNTs are near 3.0 eV and 4.7 eV owing to σ-σ* transitions along the direction of the tubular axis. The optical gaps of sp(2)-hybridized infinitely-long armchair SWSiNTs along the tube axis direction are about 0.7 eV and 2.4 eV for Si(3,3) SWSiNTs and 0.7 eV and 2.7 eV for Si(4,4) SWSiNTs. The former peak at 0.7 eV originated from π-π* electron transitions and the latter peak at 2.4 eV or 2.7 eV originated from σ-σ* electron transitions. Meanwhile, the intensities of π-π* electron transitions are stronger than those of σ-σ* electron transitions in SWSiNTs. The low sp(2) transition energy derived from the weak overlap of unpaired p(z) orbitals of silicon atoms. Moreover, the electronic excitations of zigzag SWSiNTs are similar to those of armchair structures. This indicates that sp(2)-hybridized silicon nanotubes possess much greater potential for application in optical fields.