To study the effect of transient non-thermal mobility in surface-subsurface heterogeneous catalytic reaction, simulation work has been done for CO-O2 and CO- NO catalytic reaction on different surfaces. One class of transient non-thermal mobility of species includes Ely-Rideal (ER) mechanism. The first simple lattice gas model was introduced by Ziff, Gulari and Barshad, as a computer simulation model and is known as the ZGB model, which was used to study CO- O2 reaction system. It has been found through simulation that ER mechanism generates features in the ZGB model that brings it closer to the real system. The Consideration of ER mechanism annihilates second order phase transition of the ZGB model and the reaction rate begins to increase as soon as feed concentration CO departs from zero, which is consistent with the experimental results. The other class of transient non-thermal mobility is precursor mechanism. This mechanism adds some additional features in the phase diagram of a particular catalytic reaction, which could not be observed by considering the Langmuir-Hinshelwood mechanism. In the precursor mechanism, three different ranges of the surface environment have been investigated. Each environment consists of specific pattern for set of sites around the striking site. It is observed that the reactive window depends on the mobility of the precursors. It is also observed that when the probability of the precursor is increased, the production rates increases. Furthermore, the simulation is also performed to investigate the effect of diffusion of CO on the ZGB model. It has been found that the effect of diffusion of CO on the ZGB model is to increase the mobility of CO on the surface and hence the reaction rate increases with the result that the transition point y2 shifts towards higher concentration of CO. However, the effect of diffusion of CO has no effect on the second order phase transition point y1. The effect of diffusion of CO and N (atom) for CO-NO catalytic reaction has also been studied on BCC lattice. The effect of diffusion of CO and N on the production rates is found in the high concentration of CO. This mechanism is found responsible for slight increase in the window width where the concentration of CO is high. Through these models some experimental results have been reproduced of the real system.