Three-dimensional (3D) grain sizes and size distribution functions (SDFs) are generally obtained by converting the 2D or ID grain sizes to 3D with the methods based on a spherical grain shape model (S-model), which can produce large systematic errors. In this report, a new polyhedral grain model (P-model) is developed and experimentally checked with the directly measured 3D grain sizes. The results show that the systematic error originating from the S-model can be corrected by using the new polyhedral grain model.