Coffee production is an important agriculture activity which contributes significantly to the economic growth of many countries in the world. One of the major constraints to coffee production throughout the world is the damage caused by the coffee berry borer (CBB), Hypothenemus hampei (Coleoptera: Scolytidae). It is the most damaging insect pest to coffee production in the world. These insects infest coffee berries, preferably mature berries, and spend most of their life cycle inside the berries, which make them quite difficult to control. In this work, we introduce and analyse a berry age-structured model describing the infestation dynamics of coffee berries by CBB. Using the semigroup theory in the case of Lipschitz perturbation, we show that the model has a unique nonnegative and bounded solution. We derive an explicit formula of the basic reproduction number, R0, using the next generation approach and the biological interpretation of this threshold in a specific case. Numerical simulations are carried out to illustrate the theoretical results.