The main objective of this study is to design an effective robust controller for both slewing maneuver and vibration suppression control of flexible spacecraft. In this study, the QFT robust control theory is applied to control both slewing maneuver and vibration suppression using a reaction wheel for the derived transfer function of the model including modeling uncertainty. The mathematical model is obtained using FEM(Finite Element Method) for a flexible spacecraft consisting of a reaction wheel mounted on a hub and two identical solar arrays to which sensor are attached. Vibrational mode shapes and open loop responses are simulated using the dynamical model. The QFT robust control design technique is developed to control slewing maneuver and vibration suppression for the flexible spacecraft model with interval plant considering not only stability-robustness but also control performance. Numerical simulation is then carried out for pitch axis closed-loop control system design. It is shown that the designed control system with the proposed configuration gives satisfactory results in gain margin, phase margin, and steady state tracking performance for the flexible spacecraft, respectively, also, effectively controls stewing maneuver and vibration suppression.