The density functional theory calculations for the NO-CO reaction on Rh(111) surface are carried out. The reaction pathway and the activation energy of the reaction are investigated by employing the climbing image nudged elastic band method. The rate determining step in the elementary steps of the reaction is the NO dissociation. Detailed analyses of the calculation results, such as the snapshot of the atomic configuration during the reaction, the partial density of states, and the charge density distribution, reveal what will decide the catalytic activities of NO-CO reaction. The difference of adsorption energies of NO on Rh and Cu surfaces causes the relative merit of the catalytic activity. The oxygen adsorption ability of the surface is one of the important factors to decide the catalytic activity of NO-CO reaction. The strong adsorption of an O atom inhibits the CO2 composition, on the other hand, the weak adsorption of an O atom inhibits the NO dissociation. The guidelines for searching of the alternative catalysts can be made based on the density functional theory calculations.