Currently, three-dimensional (3D) laser-scanned point clouds have been broadly applied in many important fields, such as non-contact measurements and reverse engineering. However, it is a huge challenge to efficiently and precisely extract the boundary features of unorganized point cloud data with strong randomness and distinct uncertainty. Therefore, a novel type of boundary extraction method will be developed based on concurrent Delaunay triangular meshes (CDTMs), which adds the vertex-angles of all CDTMs around a common data point together as an evaluation index to judge whether this targeted point will appear at boundary regions. Based on the statistical analyses on the CDTM numbers of every data point, another new type of CDTM-based boundary extraction method will be further improved by filtering out most of potential non-edge points in advance. Then these two CDTM-based methods and popular α-shape method will be employed in conducting boundary extractions on several point cloud datasets for comparatively analyzing and discussing their extraction accuracies and time consumptions in detail. Finally, all obtained results can strongly demonstrate that both these two CDTM-based methods present superior accuracies and strong robustness in extracting the boundary features of various unorganized point clouds, but the statistically improved version can greatly reduce time consumption.