The present paper investigates the force-extension behavior of a stiff polymer under stretching inside a small tube. We develop a theory and perform Brownian dynamic simulations based on a recently developed generalized bead-rod model (GBR) to show that the force-extension relation of such a strongly confined polymer chain can be described by that of an unconfined polymer subject to an effective force which is derived based on Odijk's theory of a confined polymer chain.