Gossamer or inflatable structures have been a subject of renewed interest for space applications because of their lightweight, on-orbit deployability, and minimal stowage volume. For these structures to be effective, their vibration must be controlled while maintaining the low weight and the foldability criteria. Piezoelectric materials have become strong candidates for actuator and sensor applications in the active vibration control of such structures due to their lightweight, conformability to the host structure, and distributed nature. In this study, vibration suppression of an inflated toroidal structure using piezoelectric actuators and sensors has been attempted. First, following the Sanders' shell theory, the governing equations of motion of a shell under pressure in the presence of piezoelectric patches have been presented, and the actuator/sensor equations are obtained. A sliding mode controller and a sliding mode observer are designed to suppress the vibration of the inflated toroidal structure using Macro-Fiber Composite (MFC) actuators and Polyvinylidene Fluoride (PVDF) sensors. The numerical simulations show that the piezoelectric actuators and sensors are suitable for vibration suppression of an inflatable structure. The robustness properties of the controller and observer against the parameter uncertainty and disturbances are also studied.