We performed the density functional calculation of bulk β-Ni(OH)2 and monolayer Ni(OH)2 as a surface model to investigate their chemical features. The nickel hydroxide (Ni(OH)2) and nickel oxyhydroxide (NiOOH) redox pair is one of the most attractive materials for electrocatalytic oxygen evolving reaction (OER) with low overpotential. However, its reaction mechanism has not yet been fully understood. Their band structures and visualized pseudo-charge density contributions indicate hydrogen interaction between the layers in the β-Ni(OH)2. In the experimental electrocatalytic OER reaction, the Fe atom is required; the structure is called NiFe-layered double hydroxide (LDH). We report the Fe effect in the monolayer Ni(OH)2 framework as the surface model of NiFe-LDH. The Fe atom is suitable for receiving electrons from substrate waters. This study provides crucial basic information for the OER mechanism on the surface of Ni(OH)2/NiOOH redox pairs.