Tuberculosis (TB) is among the main public health challenges in Burundi. The literature lacks mathematical models for key parameter estimates of TB transmission dynamics in Burundi. In this paper, the supectible-exposed-infected-recovered (SEIR) model is used to investigate the transmission dynamics of tuberculosis in Burundi. Using the next generation method, we calculated the basic reproduction number, R0. The model is demonstrated to have a disease-free equilibrium (DEF) that is locally and globally asymptotically stable. When the corresponding reproduction threshold quantity approaches unity, the model enters an endemic equilibrium (EE). That means, the disease can be controlled through different interventions in Burundi. A sensitivity analysis of the model parameters was also investigated. It shows that the progression rate from latent to becoming infectious had the highest positive sensitivity, which means that R0 increases and decreases proportionally with an increase and a decrease of that progression rate.