There are many symmetric objects in the real world. Three-dimensional (3D) laser scanning equipment can be used to obtain a 3D point cloud of symmetric objects; however, the 3D point cloud defects are easily caused by occlusion factors and the equipment itself. To resolve this problem, this paper proposes an incomplete laser 3D point cloud classification and completion approach based on object symmetry. Herein, according to the symmetric key points in a single two-dimensional image, a mapping relationship of the symmetric plane was established, and the incomplete point cloud was classified by the position of the symmetric plane in the point cloud. Moreover, for a half residual defect point cloud, symmetric plane detection was performed directly followed by the image completion. For a less than half-incomplete point cloud, it was fused with the mirror point cloud to remove the duplicated data points for image completion. Furthermore, for a greater than half-incomplete point cloud, the direct hole-repair method was used to complete the missing information after fusion with the mirror point cloud. For extremely defective point clouds, the input point cloud was fused with the mirror point cloud and then fused with a completed similar point cloud as too much information was missing. Finally, redundant points were removed to complete the missing information. The experimental results of the actual acquisition point cloud of the incomplete 3D point cloud and the point cloud in the public database show that the proposed approach can complete different types of incomplete point clouds. These results are very similar to that of the entire complete point clouds. Thus, here, the effectiveness and feasibility of the proposed classification and completion approach are verified.