The immersed boundary-lattice Boltzmann method (IB-LBM) has been verified to be an effective tool for fluid-structure interaction (FSI) simulation associated with thin and flexible body, and the newly developed smoothed point interpolation method (S-PIM) can handle the largely deformable solids owing to its soften model stiffness of model and insensitivity to mesh distortion. In this work, a novel method has been proposed by coupling IB-LBM with S-PIM for FSI problems with large-displacement solids. The proposed method preserves the efficiency of LBM for fluid solver, utilizes S-PIM to establish the realistic constitutive laws for nonlinear solids, and avoids the mesh regeneration based on the frame of immersed boundary method (IBM). Three benchmarking examples have been carried out to validate the accuracy, convergence and stability of the proposed method in consideration of comparative results with referenced solutions.