A numerical framework is proposed to couple the finite element and lattice Boltzmann methods for simulating fluid-structure interaction problems. The lattice Boltzmann method is used as an efficient method for solving the weakly-compressible fluid flows. The non-linear finite element with the explicit Newmark scheme for time integration is used to solve the structural deformation. The two methods are coupled via a direct-forcing immersed boundary method with a subiteration scheme. Validations of the proposed coupling method have been carried out by testing a vortex induced vibration problem. A good agreement is found with the reference results. This work was supported by JSPS KAKENHI Grant Numbers 16K18331.