For the new sandglass-type FPSO, the unique shape of its floating body with oblique side and external expansion can significantly improve the motion performance, but meanwhile may result in specific slamming characteristics in waves. On this basis, this paper establishes a CFD method including numerical wave-tank technique based on the Open FOAM platform. Therein, the velocity-inlet boundary method and the active absorption method are applied for numerical wave-making and wave-absorption. Compared with experimental results, the numerical method can be validated to be accurate enough to simulate wave slamming on floating ocean platforms. Then, the specific slamming phenomena on the sandglass-type floating body under a classic long wave can be investigated by comparing with the cylindrical model, including nonlinear wave rollover and breaking, water cushion, rooster-tail wave, side wave, water tongue, and so on. The mechanism of these phenomena and their effects on slamming pressure are studied. The essences of typical peaks in the time-history curve of the slamming pressure are mainly discussed. More interestingly, the main peak can be found to be related to the small peak due the amount of the broken water and the thickness of the water cushion. Finally, the slamming characteristics of the sandglass-type model in a classic short-wave condition are comparatively discussed.