Coffee is an important cash crop cultivated in the tropics, which sustains the livelihood of not less than 125 million people worldwide. However, coffee plantations are subject to various diseases, among which coffee leaf rust (CLR), caused by fungus Hemileia vastatrix, which infects coffee leaves and can severely reduce coffee berry production. We developed a deterministic ODE model which describes the interaction between CLR and coffee branches in a coffee plantation. It is based on the classical SEIR epidemiological model, with an extra state variable for spores released by infected branches, which in turn infect susceptible branches. Moreover, coffee branches are subdivided into young and mature branches, the latter producing coffee berries. We computed the basic reproduction number R0, which classically determines the stability of the disease-free equilibrium (DFE), and studied the bifurcation around R0 = 1 using Castillo-Chavez and Song’s theorem.