A Concurrent Multi-Process Refinement method for fluid-structure interaction (FSI) problems is developed and applied in a SIMPLE-based monolithic implicit method (SBMIM) initially presented by Hu et al. (2016). Concurrent Multi-Process Refinement method refines the computational domain of FSI simulations as several subdomains in multi-processes with multi-grid sizes and multi-time steps. Through file mapping, velocity and pressure data are transmitted between two processes using proper interpolations and time advance strategy. Numerical implementation and algorithm procedure of the method are explained in detail. Simulations of the liquid sloshing in a baffled tank are conducted to give an error estimation on different grid systems using the Grid Convergence Index (GCI). Simulations of the dam breaking flow slamming a vertical wall are conducted to verify the accuracy of present methods and to discuss the area selection of the localized FSI simulation. Simulations of the green water impact caused by freak wave are conducted to show the performance of this method in dealing with multi-scale ocean engineering problems and high-frequency structural vibrations. From results, it is seen that Concurrent Multi-Process Refinement method shows advantages in multi-scale FSI simulations using monolithic FSI methods and in predicting high-frequency structural vibrations, especially with low-cost computational facilities.