Modeling real-world trees is important in many application areas, including computer graphics, botany and forestry. An example of a modeling method is reconstruction from light detection and ranging (LiDAR) scans. In contrast to terrestrial LiDAR systems, airborne LiDAR systems – even current high-resolution systems – capture only very few samples on tree branches, which makes the reconstruction of trees from airborne LiDAR a challenging task. In this paper, we present a new method to model plausible trees with fine details from airborne LiDAR point clouds. To reconstruct tree models, first, we use a normalized cut method to segment an individual tree point cloud. Then, trunk points are added to supplement the incomplete point cloud, and a connected graph is constructed by searching sufficient nearest neighbors for each point. Based on the observation of real-world trees, a direction field is created to restrict branch directions. Then, branch skeletons are constructed using a bottom-up greedy algorithm with a priority queue, and leaves are arranged according to phyllotaxis. We demonstrate our method on a variety of examples and show that it can generate a plausible tree model in less than one second, in addition to preserving features of the original point cloud.