Abstract: To describe strongly coupled flow-induced vibration of a slender structure in incompressible viscous flow, this paper establishes Lagrangian-Eulerian formulations based on a generalized variational principle of coupling fluid and solid dynamics with power dissipative balance. The formulations are discretized spatially into multi-linear interpolating functions in the finite element method for fluid and solid structure. Hughes’ predictor multi-corrector algorithm for flow and Newmark’s method for vibration are monolithically combined to construct a stabilized computational method of solving the strongly coupled flow-induced vibration with complex geometry. A three-dimensional hydro turbine blade passage is taken as a numerical example to validate the method proposed in this paper. Good agreement between simulations and measurements of the pressure and vibration acceleration indicates that the method is appropriate to analyze the flow-induced vibration of a structure with complex geometry.