This paper studies a control of the extending flexible space structures. Firstly, it introduces an equation of motion of the flexible satellite by finite element method and shows that it is a linear time-varying system. Then it is represented as a linear parameter varying system and gain-scheduling control method is applied to control it. In order to design the gain-scheduling controller, the method that the scheduling parameters are preserved into a list in advance based on a finite element model, and to reduce the conservative property, the method that the range of scheduling parameters is subdivided are proposed. Finally, because of the constraint of the computer's ability, it is necessary to reduce the model's degree. So gain-scheduling control method by reducing the model's degree is described and even when the generalized plant has the model error, it is shown to be applicable by adding the robust property with the constant matrix scaling. The availability of the proposed methods is proved through numerical simulations.