An algorithm for coupling the smoothed particle hydrodynamics (SPH) method and the finite element method (FEM) is proposed for fluid-structure interaction (FSI) problems. The SPH module solves the fluid motion, and the FEM module describes the deformation of structures. In the algorithm, a structure is considered as a solid boundary in the SPH module and dealt with using the dynamic boundary condition. Only three layers of SPH boundary particles are set to represent the structure surface, and the interaction forces between the SPH boundary and fluid particles, including the water pressure and the viscous shear stress, are quantified in a same way as the inter-fluid particle forces. Further, the computed forces on the SPH boundary particles exerted by the fluid are redistributed to the structure FEM nodes based on a well-defined projection scheme. In the FEM module, the deformation and motion of the structure under the exerted fluid forces are solved, and accordingly, the position and velocity of the SPH boundary particles are updated by interpolation from the new properties at the FEM nodes. The proposed SPH-FEM coupled model is validated in three FSI benchmarks. For the deformation of an elastic plate under hydrostatic water pressure, the relative difference between the computed and the analytical maximum vertical displacement at the plate midpoint is about 1.5%. For the deformation of an elastic gate subjected to a time-varying dam-break flow, the relative root mean squared errors in the computed vertical and horizontal displacement of the gate are, respectively, 5.5% and 2.2%. It is demonstrated that the proposed model performs well in simulating the deformation of structures under both hydrostatic water pressure and dynamic impacts of dam-break flows.