Given the increase of nuclear power plants, it has become unavoidable for the pile-supported nuclear-island buildings to be constructed on the coastal deposits potentially influenced by strong earthquakes. The coupling influences of the hysteresis nonlinearity of soil and the soil-pile-structure interaction (SPSI) have not yet been considered comprehensively in the seismic response analysis of the nuclear-island building, although it is a vital issue. On the basis of a newly-developed generalized non-Masing hysteretic constitutive model, a 3D integrated simulation method is proposed to evaluate the seismic responses of the pile-mat-founded nuclear-island building system subjected to multidirectional earthquake motions. This integrated method involves an explicit parallel algorithm framework, comprising the nuclear-island building modeling, the pile-mat foundation modeling, the inhomogeneous soil domain modeling, and the artificial boundary condition. The bedrock records of near-field, moderate-far field and far-field earthquake scenarios are assumed for determining the bedrock motions of the ultimate and operational safety earthquakes. For an actual pile-mat-founded AP1000 nuclear-island building, the simulation results show the complexity and significance of the coupling effect of the site, the tridirectional earthquake shaking, and the secondary nonlinearity of soil. Such a complex coupling effect significantly increases the seismic responses of the pile-mat-founded nuclear-island building. A notable finding is that the scenario earthquakes with abundant long period components may have more destructive potential to the pile-mat-founded nuclear-island buildings than the scenario earthquakes with characteristics of abundant short period components and shorter durations. The results provide insights into the seismic design of the pile-mat-founded nuclear-island buildings, which could guide the design and construction of such similar facilities in the high seismic intensity regions.