We study an integro-difference model for a pest population with stage structure and control on each stage. When the spatial domain is infinite, we establish the spreading speeds and existence of traveling waves; when the spatial domain is finite, we first establish threshold conditions in terms of an eigenvalue of an associated eigenvalue problem to determine population persistence and extinction, and then define the net reproductive rate and develop equivalent threshold conditions for persistence and extinction by using the net reproductive rate. The cases where the reproduction function is monotone and nonmonotone are both investigated.