In three-dimensional (3D) airborne light detection and ranging (LiDAR) point-cloud data acquisition, noise point clusters (such as cloud, birds and incomplete scanning ground points) and isolated points are usually generated in the scanning process. Detection and elimination of these noise points directly affect the subsequent processing efficiency of the LiDAR point clouds. In this paper, a noise detection method from airborne LiDAR data based on spatial hierarchical directional relationship and region growing algorithm is proposed. First, the original airborne LiDAR points are divided into regular 3D grids, and the maximum point density unit is searched adaptively to select the initial surface seed points for region growing algorithm. Then, the spherical neighborhood is constructed with the initial seed point as the center, and fourteen main growth directions are generated based on the 3D space topology. Second, candidate seed points in each main direction are determined by the distance threshold. Finally, all LiDAR points are iteratively executed using candidate seed points as new region growing seed points. This paper selects two mountain terrain scenes with different cloud contents as the study area, and the precision, recall rates and F1-score of the proposed method reach 99.8%, 100% and 99.3%, respectively. This method can detect point-cloud clusters and isolated points, thus simplifying the LiDAR point clouds, providing basic support for the subsequent accurate data processing and analysis.