Planes are essential features to describe the shapes of buildings. The segmentation of a plane is significant when reconstructing a building in three dimensions. However, there is a concern about the accuracy in segmenting plane from point cloud data. The objective of this paper was to develop an effective segmentation algorithm for building planes that combines the region growing algorithm with the distance algorithm based on boundary points. The method was tested on point cloud data from a cottage and pantry as scanned using a Faro Focus 3D laser range scanner and Matterport Camera, respectively. A coarse extraction of the building plane was obtained from the region growing algorithm. The coplanar points where two planes intersect were obtained from the distance algorithm. The building plane’s optimal segmentation was then obtained by combining the coarse extraction plane points and the corresponding coplanar points. The results show that the proposed method successfully segmented the plane points of the cottage and pantry. The optimal distance thresholds using the proposed method from the uncoarse extraction plane points to each plane boundary point of cottage and pantry were 0.025 m and 0.030 m, respectively. The highest correct rate and the highest error rate of the cottage’s (pantry’s) plane segmentations using the proposed method under the optimal distance threshold were 99.93% and 2.30% (98.55% and 2.44%), respectively. The F1 score value of the cottage’s and pantry’s plane segmentations using the proposed method under the optimal distance threshold reached 97.56% and 95.75%, respectively. This method can segment different objects on the same plane, while the random sample consensus (RANSAC) algorithm causes the plane to become over-segmented. The proposed method can also extract the coplanar points at the intersection of two planes, which cannot be separated using the region growing algorithm. Although the RANSAC-RG method combining the RANSAC algorithm and the region growing algorithm can optimize the segmentation results of the RANSAC (region growing) algorithm and has little difference in segmentation effect (especially for cottage data) with the proposed method, the method still loses coplanar points at some intersection of the two planes.