We present a multigrid method for coupled fluid-solid scattering. As a smoother, we consider a Krylov method. Numerical results show that coarser spaces can be used than with standard smoothers such as Jacobi and Gauss-Seidel. We also consider block diagonal preconditioning for the $2\times 2$ block diagonal matrix of the coupled system. The iterations fail to converge for frequencies when the scatterer is at resonance. We show how to transform the system into an equivalent one which avoid the resonance.