The study of the full-scale wave–structure interaction is essential to our understanding of the nonlinear characteristics of offshore structures in real-sea states. This paper deals with full-scale numerical studies of the interactions between focusing waves and a fixed floating production storage and offloading (FPSO) in an efficient potential-viscous coupled method. The potential-viscous method combines in-house computational fluid dynamics code developed at Shanghai Jiao Tong University (SJTU) for naval architecture and ocean engineering (naoe) based on an open field operation and manipulation (FOAM), i.e., naoe-FOAM-SJTU solver, with high-order spectral method. The approach is verified on a model-scaled case and shows reasonably good agreement with experimental data. A phase-separation method and a dynamic mode decomposition method are utilized to extract linear and higher-order harmonic components from the scattering waves. The scattering waves around the FPSO are found to affect the higher-order harmonic components. Two kinds of scale ratios are considered to magnify the focusing wave and FPSO by 10 and 100 times to discuss the scale effect, both non-breaking and green water conditions are included to investigate the flow phenomenon. The harmonic components of scattering waves are not proportional to the scale ratio, and the scale effects influence more on higher-order harmonic components. The third- and fourth-order harmonic components of scattering waves around the FPSO in large-scale cases are obvious.