The coupling and interactions between ship motion and inner-tank sloshing are investigated by a potential-viscous hybrid method in 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 frequency domain. Then, the corresponding simulations of motions in time domain are carried out using the convolution-integral method. The liquid sloshing in a tank is simulated in time domain by a Navier-Stokes solver. A finite difference method with SURF scheme, assuming a singlevalued 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, linear inner-fluid motion was calculated using a 3D panel program and it is coupled with the vessel motion program in the frequency domain. The developed computer programs are applied to a barge-type FPSO hull equipped with two partially filled tanks. The time domain simulation results show reasonably good agreement when compared with MARIN's experimental results. The frequency domain results qualitatively reproduce the trend of coupling effects but the peaks are usually over-predicted. 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 to roll motions. A developed program is also applied to a more realistic offloading configuration where a LNG-carrier is moored with a floating terminal in a side-by-side configuration. First, a hydrodynamic interaction problem between two bodies is solved successfully in frequency and time domain. A realistic mooring system, including fender, hawser, and simplified mooring system, is also developed to calculate the nonlinear behavior of two bodies in time domain simulation. Then, the LNG-carrier and sloshing problem are coupled in frequency and time domain, similar to the method in the MARIN-FPSO case. Sloshing effect on LNG-carrier motion is investigated with respect to different tank filling levels including various conditions such as gap distance between two bodies, selection of dolphin mooring system, and different cases of environmental conditions using wave, wind, and current.