In recent years, China has constructed numerous large-scale underground projects. To ensure construction quality, it is essential to quickly assess the safety status of the steel-reinforced concrete columns in these underground projects. For this purpose, point cloud data obtained from ground-based three-dimensional (3D) laser scanners are used for detection. First, the point cloud data are concatenated and extracted. Then, the momentum gradient descent method is employed to fit the cylinder equation to the point cloud data, and the verticality of the cylinder is calculated based on the direction and vertical vectors derived from the fitted cylinder equation. Finally, Three groups of experiments are conducted on the steel-reinforced concrete columns of the underground comprehensive transportation hub project. In the first two groups, momentum gradient descent is used to perform the fitting and compute the perpendicularity, and the results are compared with the point cloud data using multi-station stitching and single-station cloud data. The third group uses a total station to measure verticality, and the results are treated as near-truth values. The experimental results are summarized as follows: (1) The accuracy of the verticality calculated using the momentum gradient descent fitting method meets the measurement requirements specified in relevant engineering standards compared with the total station measurement results. (2) Both multi-station and single-station point cloud data are sufficient for satisfying the measurement requirements. (3) The proposed method improves the work efficiency by four times compared to the traditional detection methods. These experimental results demonstrate that the 3D laser scanner offers strong potential and practical feasibility for the rapid measurement of column verticality, providing valuable support for the rapid detection of column verticality in subsequent construction and completion.