In this work we propose a Robin-Robin preconditioner combined with Krylov iterations for the solution of the interface system arising in fluid-structure interaction (FSI) problems. It can be seen as a partitioned FSI procedure and in this respect it generalizes the ideas introduced in [Badia, Nobile and Vergara, J. Comput. Phys. 227 (2008) 7027 –7051]. We analyze the convergence of GMRES iterations with the Robin-Robin preconditioner on a model problem and compare its efficiency with some existing algorithms. The method is shown to be very efficient for many challenging fluid-structure interaction problems, such as those characterized by a large added-mass effect or by enclosed fluids. In particular, the possibility to solve balloon-type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches.