Adsorption of water on (001)-terminated α-V₂O₅ surface has been investigated in the framework of density functional theory. According to our calculations, molecular adsorption is preferred, and two types of adsorption sites (Lewis acid center on V atom and Lewis base center on O atoms) have been found. Water adsorption on Lewis acid site does not change the electronic structure of V₂O₅ surface. Adsorption on Lewis base site is less favorable but reduces the band gap value by half (from 2.5 to 1.3 eV). The reason of this decreasing is the localization of the non-bonding 1b₂ electron state of water molecule within the forbidden gap of V₂O₅ surface. The idealized structure of V₂O₅∙nH₂O xerogel has been computationally studied at n = 0 and 1. It is proved that only Lewis base sites are suitable for water positions. At n = 1, the water absorption energy in xerogel is close to adsorption energy of water on the oxygen atoms of α-V₂O₅ surface. The presence of the non-bonding states of physically absorbed water in the forbidden gap is also found in the xerogel case. This results in decreasing of the band gap from 2.7 eV to 0.7 eV.