The most important aspect of digital terrain model generation from airborne laser scanning (ALS) data is that of filtering a point cloud to obtain ground points. Numerous automatic filters have been proposed since ALS data became available. However, to filter out nonground points, a slope threshold is usually introduced to classify points into ground and nonground points; this leads to frequent over-filtering problems in cliff-like terrains. A solution to this problem is proposed, using a dual-directional slope-based filter originating from a conventional slope-based filter is proposed. This filter is designed as a directional filter in one dimension and is applied to every profile of light detection and ranging (LiDAR) points. In this process, a directional filter is first applied to the profile, and another directional filter is then applied at an angle of 180 deg from the first one. Each directional slope-based filter is complementary to the others, thus avoiding over-filtering. We utilize ISPRS LiDAR data for the test. A comparison of this filter approach with existing methods is presented. The comparison result shows that the proposed method obtains a classification accuracy that is as good as most of the compared methods, but is superior to them with regard to handling data from abrupt surfaces.