In this paper, a new predictive model for the ice layer and water film growth, which occurs due to seawater spray impinging on large horizontal surfaces of a supply vessel, is developed using a Stefan-type problem formulation. The icing model includes conduction heat transfer in the ice and brine film layer, assuming the volume and distribution of brine pockets and air bubbles within the ice accumulation are uniform. The model also uses heat and mass balances to predict the freezing fraction, temperature distribution, ice layer and water film thickness. The results show that the water film salinity and icing intensity change with time during the icing period. Additionally, the water film salinity variations affect the freezing temperature, thermal conductivity and specific heat capacity of ice formation. As a result, heat conduction within the accumulated ice changes with time due to the variations of salinity; thus, the conduction heat flux has a significant effect on the ice thickness growth rate. This new model is a useful tool for forecasting and assessing the potential ice accumulation on marine vessels and structures.