Optical properties of hydrogenated silicon clusters are investigated by density functional pseudopotential calculation. Transitions between the band-edge orbitals are allowed, in contrast to the indirect gap in bulk silicon. The energy gaps of hydrogenated silicon particles of 15 to 30 Å in diameter are estimated to be 2.0 to 1.5 eV. When the cluster is dehydrogenated, localized states related to dangling bonds appear in the mid-gap, which decrease the photoluminescence intensity. These results agree with much experimental evidence and suggest that the photoluminescence of porous silicon is attributable to hydrogenated silicon particles.