This study focuses on finding high-performance numerical solutions to fluid–structure coupling problems encountered in biomechanical engineering. A numerical framework for simulating fluid–structure interaction (FSI) is proposed by strongly coupling the finite element and lattice Boltzmann methods. The lattice Boltzmann method is efficient for solving weakly compressible fluid flows. The explicit finite element method (FEM) is used to solve solid structure deformation. A partitioned iterative solution is adopted to couple these two methods together. A fixed point iteration method is used with the Aitken dynamic relaxation algorithm to improve numerical stability. A multi-direct forcing immersed boundary method with a sub-iteration scheme is adopted to represent the interaction between fluid and structure. Validation of the proposed coupling method was conducted on a vortex induced vibration problem. The numerical results are in good agreement with the reference results (Li and Favier, 2017). The proposed method does not have to solve large systems of linear equations, so it is suited to parallel computation. Therefore, we then present a parallel implementation of our method on a graphics processing unit, which increases the computation speed more than 18-fold. Our developed FSI solver is very efficient, which makes it possible to provide more accurate results with finer meshes. Finally, our method is applied to the simulation of complicated motions of a bileaflet heart valve caused by blood flow.