This paper studies the problem of stabilization of extending space structures. We derive the equations of motion of the structure extending in orbit under the gravity gradient torque environment. Because the equation is a time-varying system, the existing condition of gravity gradient stabilization developed for the non-extending system is not valid for the case. Therefore we newly derive a stability condition of time-varying systems, based on which the asymptotically stabilizing control law is derived. The obtained result is confirmed by some simulations. It is also shown that the same stability condition is applicable when the structure has physical parameter errors.