Complete removal of water from room-temperature ionic liquids is nearly impossible. For the electrochemical applications of ionic liquids, how water is distributed in the electrical double layers when the bulk liquids are not perfectly dry can potentially determine whether key advantages of ionic liquids, such as a wide electrochemical window, can be harnessed in practical systems. In this paper, we study the adsorption of water on electrode surfaces in contact with humid, imidazolium-based ionic liquids using molecular dynamics simulations. The results revealed that water molecules tend to accumulate within sub-nanometer distance from charged electrodes. At low amount of water in the bulk, the distributions of ions and of electrostatic potential in the double layer are affected weakly by the presence of water, but the spatial distribution of water molecules is strongly dependent on both. The preferential positions of water molecules in double layers are determined by the balance of several factors: the tendency to follow the positions of the maximal absolute value of the electrical field, the association with their ionic surroundings, and the propensity to settle at positions where more free space is available. The balance between these factors changes with charging the electrode, but the adsorption of water generally increases with voltage. The ion specificity of water electrosorption is manifested in the stronger presence of water near positive electrodes (where anions are the counterions) than near negative electrodes (where cations are counterions). These predictions await experimental verification.