A seismic response analysis method for three-dimensional floating offshore structures due to seaquakes is developed. The hydrodynamic pressure exerted on the structure is calculated taking into account the compressibility of the sea water, the fluid-structure interaction, the energy absorption by the seabed, and the energy radiation into infinity. To validate developed method, the hydrodynamic pressure induced by the vibration of a floating massless rigid circular disk is calculated and compared with an exact analytical solution. The developed method is applied to seismic analysis of a support structure for a floating offshore wind turbine subjected to the hydrodynamic pressures induced from a seaquake. Analysis results show that earthquake response of a floating offshore structure can be greatly influenced by the compressibility of fluid, the depth (natural frequencies) of the fluid domain, and the energy absorption capacity of the seabed.