Aiming at the inefficiency caused by the optimal design of rotationally symmetric horn feed models, a fast modeling method for rotationally symmetric structures is proposed, which is used to deal with the mesh generation of rotationally symmetric structures and the rapid establishment of computational models. In this paper, the body-of-revolution finite-difference time-domain (BOR–FDTD) method is employed to investigate the radiation performance of the horn feed. Due to the rotational symmetry of the horn antenna, modeling only requires the establishment of a two-dimensional cross-sectional mesh of the horn feed. An optimized Delaunay triangulation algorithm combined with the projection intersection method is utilized to triangulate the horn cross-section of arbitrary polygons and establish the BOR–FDTD computational mesh. Results from both single-medium and multi-medium triangulation algorithms and computational models verify the accuracy of this modeling method. The radiation patterns of a smooth-walled horn were calculated and compared with the modeling time of MATLAB 2017 and the simulation time of CST. The results reveal that the algorithm presented in this paper aligns well with the simulation results from CST; furthermore, the modeling time amounts to only 6.78% of the MATLAB program’s modeling time, while the total simulation time is 31.3% of CST, which demonstrates both the accuracy and efficiency of the proposed method.