A control oriented model of the Lean $NO_x$ trap (LNT) was developed to determine the timing of $NO_x$ regeneration. The LNT model consists of $NO_x$ storage and reduction model. Once $NO_x$ is stored ($NO_x$ storage model), at the right timing $NO_x$ should be released and then reduced ($NO_x$ reduction model) with reductants on the catalyst active sites, called regeneration. The $NO_x$ storage model simulates the degree of stored $NO_x$ in the LNT. It is structured by an instantaneous $NO_x$ storage efficiency and the $NO_x$ storage capacity model. The $NO_x$ storge capacity model was modeled to have a Gaussian distribution with a function of exhaust gas temperature. $NO_x$ release and reduction reactions for the $NO_x$ reduction model were modeled as Arrhenius equations. The parameter identification was optimally performed by the data of the bench flow reactor test results at space velocity 50,000/hr, 80,000/hr, and temperature of $250-500^{circ}C$. The LNT model state, storage fraction indicates the degree of stored $NO_x$ in the LNT and thus, the timing of the regeneration can be determined based on it. For practical purpose, this model will be verified more completely by engine test data which simulate the NEDC transient mode.