Busseola fusca is a maize and sorghum pest that can cause significant damage to both crops. Given that maize is one of the main cereals grown in the worldwide, this pest is a major challenge for maize production and therefore for the economies of several countries . In this paper , based on the life cycle of B. fusca, we propose a mathematical model to study the population dynamics of this insect pest . A sensitivity analysis using the eFast method was performed to show the most important parameters of the model. We present the theoretical analysis of the model. More precisely, we derive a threshold parameter N0, called basic offspring number and show that the trivial equilibrium is globally asymptotically stable whenever N0≤1, while if N0>1, the non trivial equilibrium is globally asymptotically stable. The theoretical results are supported by numerical simulations.