The boundary stabilization of a coupled fluid-structure system consisting of a vibrating parachute dam in contact with a fluid is studied in this paper. The parachute dam dynamics is presented by nonlinear partial differential equations. The fluid is assumed to be Newtonian, barotropic, and compressible. For the stability analysis of the coupled system, the boundary control method is used; a boundary feedback is constructed to stabilize the vibrations of the dam and the fluid simultaneously. The control force consists of the feedback from dam tension at its end. Moreover, the exponential stabilization of the parachute dam is achieved using a Lyapunov functional and boundary feedback.