The capability of acquiring accurate and dense three-dimensional geospatial information that covers large survey areas rapidly enables airborne light detection and ranging (LiDAR) has become a powerful technology in numerous fields of geospatial applications and analysis. LiDAR data filtering is the first and essential step for digital elevation model generation, land cover classification, and object reconstruction. The morphological filtering approaches have the advantages of simple concepts and easy implementation, which are able to filter non-ground points effectively. However, the filtering quality of morphological approaches is sensitive to the structuring elements that are the key factors for the filtering success of mathematical operations. Aiming to deal with the dependence on the selection of structuring elements, this paper proposes a novel filter of LiDAR point clouds based on geodesic transformations of mathematical morphology. In comparison to traditional morphological transformations, the geodesic transformations only use the elementary structuring element and converge after a finite number of iterations. Therefore, this algorithm makes it unnecessary to select different window sizes or determine the maximum window size, which can enhance the robustness and automation for unknown environments. Experimental results indicate that the new filtering method has promising and competitive performance for diverse landscapes, which can effectively preserve terrain details and filter non-ground points in various complicated environments