This study presents an approach for extracting boundaries of various buildings, which have concave boundaries, inner yards, non-right-angled corners, and nonlinear edges. The approach comprises four steps: building point segmentation, boundary tracing, boundary grouping, and regularization. In the second and third steps, conventional algorithms are improved for more accurate boundary extraction, and in the final step, a new algorithm is presented to extract nonlinear edges. The unique characteristics of airborne light detection and ranging (LIDAR) data are considered in some steps. The performance and practicality of the presented algorithm were evaluated for buildings of various shapes, and the average omission and commission error of building polygon areas were 0.038 and 0.033, respectively.