The electronic structures of hydrogen-passivated single-crystalline silicon nanotubes (Hsc-SiNTs) along the [100], [110], [111], and [112] directions and the absorption spectra of [100]-oriented Hsc-SiNTs are studied by using density functional theory within the generalized gradient approximation. We find that the band gaps of the Hsc-SiNTs generally increase with decreasing wall thickness because of the quantum confinement effects. But when the inner radii of the tubes are extremely small, the quantum confinement effects are weakened significantly by the adsorbed hydrogen atoms. In addition, the band gaps of the Hsc-SiNTs along the [100], [110], and [111] directions are all direct at small sizes, whereas those of the [112]-oriented tubes remain indirect. We also find that the magnitude of the band gap of the Hsc-SiNTs also depends on the tube orientation and morphology. Compared with the absorption spectra of hydrogen-passivated single-crystalline [100]-oriented silicon nanowires with an identical external diameter, a split of the original peak and an overall blue shift are observed in the absorption spectra of [100]-oriented Hsc-SiNTs.