Plane segmentation is a simple yet essential processing step for using 3D point clouds in applications such as temporal data registration and object modeling. The performance of traditional plane segmentation algorithms, especially when addressing photogrammetric point clouds, is significantly limited by factors including the errors of the point positions, noise contamination, and unevenly distributed density, resulting in a low segmentation efficiency and poor segmentation outcome. This paper proposes a robust plane segmentation algorithm for addressing photogrammetric point clouds of construction site scenarios. The implementation of the proposed method includes three major steps: preprocessing, segmentation of the point clouds, and extraction of the planes. The preprocessing is designed to suppress noise and filter outliers, and downsample the dataset. In the subsequent segmentation step, we propose a bottom-up approach utilizing the voxelized structure and facet-based global clustering to obtain planar segments using an automatic and unsupervised clustering of the planar facets selected from the voxelized points. In the last step, the points of the planar segments are extracted using a parametric model-based plane fitting. A 3D Hough transform-based method, constrained by an orientated bounding box, is developed to generate the initial model of the planes. The obtained plane models are then localized by the oriented bounding box and optimized by a local clustering-based plane refinement. The experimental results using synthetic datasets and a low-cluttered laser scanning dataset confirm that the proposed method is superior to the traditional algorithms in key criteria including calculation time, extraction precision, and recall. For real applications on two datasets of different construction sites, the proposed method could segment the majority of the structural planes from the points, with accurate model parameters, sizes, and locations estimated.