The immersed boundary lattice-Boltzmann lattice-spring method (IBLLM) has previously been implemented to solve several systems involving deformable and moving solid bodies suspended in Navier-Stokes fluids, but these studies have generally been limited in scope by a lack of computing power. In this study a Graphics Processing Unit (GPU) in CUDA Fortran is implemented to solve a variety of systems, including a flexible beam, stretching of a red blood cell (RBC), and an ellipsoid under shear flow. A series of simulations is run to validate implementation of the IBLLM and analyze computing performance. Results demonstrate that an Intel Xeon E5645 fitted with an NVIDIA Tesla K40 graphics card running on a GPU improves computational speed by a maximum of over 80-fold increase in speed when compared with the same processor running on a CPU for solving a system of moderately sized solid and fluid particles. These studies represent the first report on using a single GPU device with CUDA Fortran in the implementation of the IBLLM solver. Incorporation of a GPU while solving with the versatile IBLLM technique will expand the range of complex fluid-solid interaction (FSI) problems that can be solved in a variety of fields.