The study of liquid dynamics in LNG tanks is getting more and more important with the actual trend of LNG tankers sailing with partially filled tanks. The effect of sloshing liquid in the tanks on pressure levels at the tank walls and on the overall ship motion indicates the relevance of an accurate simulation of the fluid behaviour. This paper presents the simulation of sloshing LNG by a compressible two-phase model and the validation of the numerical model on model-scale sloshing experiments. The details of the numerical model, an improved Volume Of Fluid (iVOF) method, are presented in the paper. The program has been developed initially to study the sloshing of liquid fuel in spacecraft. The micro-gravity environment requires a very accurate and robust description of the free surface. Later, the numerical model has been used for calculations for different offshore applications, including green water loading. The model has been extended to take two-phase flow effects into account. These effects are particularly important for sloshing in tanks. The complex mixture of the liquid and gas phase around the free surface imposes a challenge to numerical simulation. The two-phase flow effects (air entrapment and entrainment) are strongly affected by both the filling ratio of the tank and the irregular motion of the tank in typical offshore conditions. The velocity field and pressure distribution around the interface of air and LNG, being continuous across the free surface, requires special attention. By using a newly-developed gravity-consistent discretisation, spurious velocities at the free surface are prevented. The equation of state applied in the compressible cells in the flow domain induces the need to keep track on the pressure distribution in both phases, as the gas density is directly coupled to the gas pressure. The numerical model is validated on a 1:10 model-scale sloshing model experiment. The paper shows the results of this validation for different filling ratios and for different types of motion of the sloshing tank.