A new method for calculating the afloat condition of convex polyhedron composite structure was pro-posed． Firstly，the afloat object was meshed by the tetrahedra，and then the water plane equation was calculated by the double iterative method，which consists of the inner and outer iterative procedures simulating the heaving and rotation motions of the afloat object respectively． The afloat condition experiment was carried out for a semi-submersible offshore platform． The algorithm proposed in this paper was also compared with Maxsurf which is the famous computer aided ship design and construction software． The experimental and comparative test results show that the method has clear physical meaning，the corresponding algorithm is accurate and reliable with good conver-gence． This new method is more suitable for analyzing the afloat condition of the convex polyhedron composite structure than the traditional method．