We study the exact controllability of a fluid-structure model. The fluctuations of fluid velocity and pressure in a domain Omega are described by a potential phi, and the structure is a membrane located in a part Gamma(s) of the boundary Gamma = partial derivative Omega of the domain Omega. The potential phi and the transverse displacement z of the membrane satisfy a coupled system of two wave equations, one in the domain Omega x (0, T) and the other one in the boundary Gamma(s) x (0, T). We take two boundary controls, the first in a Neumann boundary condition on Gamma(0) = Gamma\(Gamma) over bar (s) satisfied by the potential and the second one in a Dirichlet boundary condition of the structure equation. We show that we can drive the fluid-structure system from an initial state in some space Y to another terminal state in Y with controls in (H(1)(0, T; L(2)(Gamma 0)))' x L(2)(partial derivative Gamma(s) x (0, T)). As in the case of the so-called Helmholtz fluid-structure model [J. Raymond and M. Vannination, ESAIM Control Optim. Calc. Var., 11 (2005), pp. 180-203] and in the aeroacoustic model with Dirichlet boundary controls [L. Cot, J.-P. Raymond, and J. Vancostenoble, Exact controllability of an aeroacoustic model, in CSVAA 2004-Control Set-Valued Analysis and Applications, EDP Sci., Les Ulis, 2007, pp. 26-49], the difficulty in the treatment of the observability inequalities, in the definition of very weak solutions, and in the proof of the controllability result comes from the coupling terms of the system. We show that the variants of the classical Hilbert uniqueness method introduced in [J. Raymond and M. Vannination, ESAIM Control Optim. Calc. Var., 11 (2005), pp. 180-203] and [L. Cot, J.-P. Raymond, and J. Vancostenoble, Exact controllability of an aeroacoustic model, in CSVAA 2004-Control Set-Valued Analysis and Applications, EDP Sci., Les Ulis, 2007, pp. 26-49] can be adapted to the aeroacoustic model that we consider.