We have carried out an investigation using density functional theory (DFT) of the atomic and electronic structures of SnSe₂ layers on the surface and hydrogenation of this surface. We have considered a (2 × 2) SnSe₂ superstructure oriented along the diagonal direction of the surface periodicity, for which scanning tunneling microscopy (STM) measurements have recently been reported. In the band structure calculations, while the s–p character surface state originating from each SnSe₂ layer is determined, there is an additional half-filled surface state in the fundamental band gap region due to the Sn adatom. At the point in the Brillouin zone, a charge density wave (CDW) partial gap opening of ∼0.1 eV occurs between these surface states close to the Fermi level. Here, the CDW gap is caused by two reasons; (i) Fermi surface nesting, due to the inequivalent electron pockets at the point, and (ii) the out of plane weak electron–phonon coupling regime due to the mean-field (MF) theory (2Δ/k_BT^MF = 3.52). Upon hydrogen adsorption on the surface, we have obtained a β-phase SnSe layer and SeH₂ molecule with a bond angle of ∼90°. The hydrogenated surface pushes the surface state associated with the SnSe₂ layer into the Si projected bulk band continuum. After SeH₂ desorption, the work function drops from 5.20 eV to 4.39 eV.