The coupling and interactions between ship motion and inner-tank sloshing are investigated by a potential-viscous hybrid method in the time domain. For the time-domain simulation of vessel motion, the hydrodynamic coefficients and wave forces are obtained by a potential-theory-based 3D diffraction/radiation panel program in the frequency domain. Then, the corresponding simulations of motions in the time domain are carried out using the convolution-integral method. The liquid sloshing in a tank is simulated in the time domain by a Navier–Stokes solver. A finite difference method with SURF scheme assuming the single-valued free-surface profile is applied for the direct simulation of liquid sloshing. The computed sloshing forces and moments are then applied as external excitations to the ship motion. The calculated ship motion is in turn inputted as the excitation for liquid sloshing, which is repeated for the ensuing time steps. For comparison, we independently developed a 3D panel program for linear inner-fluid motions, and it is coupled with the vessel-motion program in the frequency domain. The developed computer programs are applied to a barge-type floating production storage and offloading (FPSO) hull equipped with two partially filled tanks. The time-domain simulation results show reasonably good agreement when compared with Maritime Research Institute Netherlands (MARIN’s) experimental results. The frequency-domain results qualitatively reproduce the trend of coupling effects, but the peaks are in general overpredicted. It is seen that the coupling effects on roll motions appreciably change with filling level. The most pronounced coupling effects on roll motions are the shift or split of peak frequencies. The pitch motions are much less influenced by the inner-fluid motion compared with roll motions.