Adsorption of a H2O molecule on Bi, Ga and Hg electrode surfaces is studied in the framework of cluster model at the density functional theory (DFT) level. At bismuth(111) single crystal plane the hollow site is energetically more preferable for the H2O adsorption (- 31.1 kJ mol- 1), while the adsorption at top site of Hg and Ga metal surfaces is confirmed to be energetically the most preferable (- 35.6 and - 24.7 kJ mol- 1, respectively). The calculations for Bi(111), Hg, and Ga are further extended to include the effect of external electrical field, and data analysis is completed with the help of the mean field approximation in order to model adsorbed water behaviour in the H2O molecules' bilayer. An associate of 13 H2O molecules is modelled in order to address the influence of lateral interactions in a water bilayer. The Ga surface is argued to be more hydrophilic than the Bi(111) and Hg surfaces. Despite the weaker adsorption energy of a single H2O molecule at the Ga surface, water molecules at the Ga/water interface are additionally stabilized by stronger hydrogen bonds. We stress the important role of the H2O bilayer at a metal electrode surface, which depends on the atomic corrugation of a metal surface.