In this paper, numerical simulations of FPSO ship motion coupled with LNG tank sloshing with low-filling ratios are conducted. The fully coupled problem is addressed with our own unsteady RANS solver: naoe-FOAM-SJTU developed based on the open source tool libraries of OpenFOAM. The internal tank sloshing and external wave flow are solved simultaneously. The FPSO model includes 2 LNG tanks. For the ship 3-DOFs are released in the regular beam waves. The filling ratios of the 2 tanks are 20%~20%, lower than the external free surface. This kind of low-filling condition reduces ship roll motion significantly, and produces complex free surface shapes in tanks. 4 different incident wave frequencies are considered in the simulation in comparison with the existing experimental data. The comparison shows that the numerical results are in good agreement with the experimental data, proving the reliability of the proposed method. The filling conditions with large wave amplitudes are studied further, and due to the coupling effect, violent sloshing occurs in tanks and impulsive pressure forms on bulkhead.