Reconstruction of 3D trees from incomplete point clouds is a challenging issue due to their large variety and natural geometric complexity. In this paper, we develop a novel method to effectively model trees from a single laser scan. First, coarse tree skeletons are extracted by utilizing the L1 -median skeleton to compute the dominant direction of each point and the local point density of the point cloud. Then we propose a data completion scheme that guides the compensation for missing data. It is an iterative optimization process based on the dominant direction of each point and local point density. Finally, we present a L1 -minimum spanning tree (MST) algorithm to refine tree skeletons from the optimized point cloud, which integrates the advantages of both L1 -median skeleton and MST algorithms. The proposed method has been validated on various point clouds captured from single laser scans. The experiment results demonstrate the effectiveness and robustness of our method for coping with complex shapes of branching structures and occlusions.