Abstract: In this paper, a discrete tuberculosis model is investigated. By means of calculating the next generation matrix'sspectral radius, we derive the reproduction number $R_0$ of themodel. The solutions of the model are bounded and positive, whichcan be verified through the relation theory of the differenceequation. It is proved that $R_0 =1$ is a threshold to determine thedisease extincation or persistence. The disease-free equilibrium isglobal asymptotically stable when the reproduction number $R_0 <1$.The endemic equilibrium is global asymptotically stable when the reproduction number $R_0 >1$