Developing low-cost, high activity and stability oxygen evolution reaction (OER) catalysts is significantly important but still challenging for water electrolyzers. In this work, we calculated the OER activity and stability of Metal-Nitrogen-Carbon (MNC, M = Co, Ru, Rh, Pd, Ir) based electrocatalyst with different structures (MN4C8, MN4C10, MN4C12) using density functional theory (DFT) method. These electrocatalysts were divided into three groups based on the value of ΔG*OH, that is ΔG*OH > 1.53 eV (PdN4C8, PdN4C10, PdN4C12), ΔG*OH < 1.23 eV (RuN4C8, RuN4C10, RuN4C12, CoN4C8, CoN4C10) and 1.23 eV < ΔG*OH < 1.53 eV (RhN4C8, RhN4C10, RhN4C12, IrN4C8, IrN4C10, IrN4C12, CoN4C12), and ΔG*OH determine whether the structure evolution will appear. The results proved that MNC (M = Rh, Ir) with 1.23 eV < ΔG*OH < 1.53 eV shows higher OER activity due to moderate binding energy between reaction intermediates and MNC. Furthermore, these catalysts could maintain MNC structure without further oxidation and structural evolution under working conditions (high temperature, dynamic condition, local electric field and strong specific adsorption), therefore show excellent stability. However, MNC electrocatalyst with ΔG*OH > 1.53 eV or ΔG*OH < 1.23 eV revealed less stability under working conditions, due to their low intrinsic stability or structural evolution under working conditions, respectively. In conclusion, we proposed a comprehensive evaluation method for MNC electrocatalysts by taking ΔG*OH as the screening criterion for OER activity and stability, as well as ΔEb under working condition as descriptor of stability. This is of great significance for the design and screening of ORR, OER and HER electrocatalysts under working conditions.