The cuboid primitive fitting is a typical problem of 3D point cloud geometric fitting, which is widely used in practical scenes, such as 3D reconstruction, reverse engineering and industrial 3D measurement. In practical applications, it is usually impossible to obtain complete cuboid point cloud data due to occlusion and equipment blind area, which makes it difficult to accurately fit cuboid structure in modeling or measurement. To solve this problem, this article proposes a cuboid parameterized fitting method which combines plane-fitting projection segmentation and incomplete plane vertical angle detection, and realizes the cuboid parameterized fitting. Firstly, the plane point cloud with strong contour information is obtained by the plane fitting projection segmentation algorithm. Then, the detection algorithm of incomplete plane vertical angle is designed to fit the real corner points of cuboids. Finally, the non-coplanar fourpoint method is used to calculate and complete the incomplete corner points of cuboids to obtain the complete cuboid parameter information. Experiments show that the proposed method can accurately detect and complete cuboid corner point information and plane parameter information in all kinds of situations. The accuracy rate and recall rate of corner point are both 100% , and the average error is only 1. 204×10 -3 m. The proposed method can achieve accurate cuboid parameterization fitting.