A torque-shaping method using trigonometric series expansion and optimization is demonstrated experimentally for a flexible space structure testbed, The hub-appendage structure is carefully designed and assembled to provide an environment to achieve the rest-to-rest maneuver and vibration suppression. The reaction wheel assembly is used as an actuator to drive the structure, while an encoder, a gyroscope, and a piezoelectric transducer are used as sensors to detect the slew/flexible motion. The experimental testbed is identified by applying an optimization technique using the data of the structure actuated by an impulsive hub control torque. With the well-adjusted experimental environment, the open-loop experiment results using the torque-shaping method match well with those of the numerical simulations. Furthermore, the closed-loop experiment results show that precise targeting is achieved in the presence of various external disturbances. The proposed method will provide an efficient basis for implementing a realizable torque-shaping strategy for the slewing of flexible space structures.