In this paper, the shaking table tests of a Seismic–Soil–Pile–Superstructure Interaction (SSPSI) in medium-soft and hard base soil were carried out. Silted clay with a unit weight of 1.70 g/cm3 and a shear wave velocity of 175 m/s was adopted to simulate the medium-soft soil, while the composite soil obtained by adding 20% quicklime to silted clay with a unit weight of 1.75 g/cm3 and a shear wave velocity of 300 m/s was adopted to simulate the hard soil in the tests. By inputting the artificial seismic motion time history with different amplitudes synthesized by the RG1.60 response spectrum commonly used in nuclear power engineering to the models, the dynamic interaction characteristics and seismic response laws of the soil–pile–nuclear island structure in the medium-soft and hard base soil were compared, the internal force and deformation distribution characteristics of the pile foundation under different ground conditions were analyzed, and the site conditions and mechanism of seismic failure of the pile group foundation were described. The research results can provide a reference for site selection and seismic design of a nuclear power plant.