The effect of co-adsorption of CO molecules in the NO-CO reaction on a metal catalytic surface like Pt(001) is studied by applying the Langmuir-Hinshelwood mechanism using the Monte Carlo simulations.The system is investigated by two approaches of NO adsorption;dissociatively at two empty surface sites and molecularly at a single vacant site. The elementary steps are the same as those in the conventional Ziff-Gulari-Barshad model.With the additional reaction step of co-adsorption,the sustained production of CO2 is obtained,which has never been seen on a square lattice without introducing additional parameters.The most interesting result is the elimination of continuous second order phase transition,i.e.the production of CO2 starts as soon as the partial pressure of CO departs from zero,which is in accordance with the experimental observations,The effect of co-adsorption probability on the phase diagrams has also been studied.