In this study we designed a lean $NO_x$ trap (LNT) model with $GT-POWER^{TM}$ program and then the LNT model was compared to the bench flow reactor test results. This model consists of 9 kinetic reactions to represent the main steps of NO oxidation, $NO_x$ adsorption, $NO_x$ release and then its reduction. The comparison was performed on the operating conditions at the space velocity of 50,000 1/hr and 80,000 1/hr with the temperature range of $200^{circ}C{sim}500^{circ}C$ with the even spaced temperature step of $50^{circ}C$. The experimental results show that the $NO_x$ conversion efficiency was enhanced by the temperature up to $350^{circ}C$ and then decayed at higher temperatures. The LNT model predicts the similar trend of the $NO_x$ conversion efficiency to the experimental results below $350^{circ}C$, but overestimates above $350^{circ}C$. This overestimation comes from the higher reduction efficiency which was obtained by the different reduction gas composition such as $C_3H_6$ in the model to replace $CH_4$, $C_2H_4$ in the bench test.