Complex multidisciplinary physical fields formed by the dynamic interaction between fluid flows, structure motion, and seabed profile evolution are natural in a marine environment. Modeling and analysis of such fluid-structure-sediment interactions are essential for predicting and analyzing the nonlinear behavior of movable structures and their surrounding sediments under wave action. However, no analytical and numerical tools which consider the detailed physics of the entire coupled fluid-structure-sediment system are currently available. In this study, a three-dimensional coupled fluid-structure-sediment interaction model is developed to provide an overarching computational framework for simulating the dynamic behavior of multidisciplinary physical systems. The model consists of an extended Navier-Stokes solver that computes incompressible viscous multiphase flow, a volume-of-fluid module that tracks air-water interface motion, an immersed boundary module that tracks structure motion, and a sediment transport module that tracks suspended sediment motion and seabed profile evolution. For validation, the model is applied to hydraulic experiments on local scouring around a movable short cylinder supported at the base. It is found that the model predicts scour patterns around the cylinder reasonably well, consistent with experimental results measured in the hydraulic experiments. In addition, the computational applicability of the model is demonstrated to predict and analyze a general complex fluid-structure-sediment interaction phenomenon in the marine environment.