Pagodas are common historical structures in China and some other Asian countries. Symmetries of the pagodas play an important role on cultural and structural aspects. In this paper, we proposed a method estimating the central axis of a typical ancient pagoda in China for examination of its symmetry. We developed a novel geometric model to fit to the point cloud of the pagoda obtained from photogrammetric reconstruction based on UAV imagery. More specifically, we developed a novel geometric model possessing 16 parameters to fit to the point cloud of different parts of the pagodas simultaneously to estimate a central axis for the symmetry. The results show that the proposed model is superior to the conventional cylindrical models for the central axis estimation. More importantly, the estimated parameters are in realistic ranges, as well as the reconstructed central axis and the sextant number are well visualized, so the symmetry of the pagodas can be readily analysed.