The outstanding accuracy and spatial resolution of airborne light detection and ranging (LiDAR) systems allow for very detailed urban monitoring. Classification is a crucial step in LiDAR data processing, as many applications, e.g., 3D city modeling, building extraction, and digital elevation model (DEM) generation, rely on classified results. In this study, we present a novel LiDAR classification approach that uses simple pixel comparison features instead of the manually designed features used in many previous studies. The proposed features are generated by the computed height difference between two randomly selected neighboring pixels. In this way, the feature design does not require prior knowledge or human effort. More importantly, the features encode contextual information and are extremely quick to compute. We apply a random forest classifier to these features and a majority analysis postprocessing step to refine the classification results. The experiments undertaken in this study achieved an overall accuracy of 87.2%, which can be considered good given that only height information from the LiDAR data was used. The results were better than those obtained by replacing the proposed features with five widely accepted man-made features. We conducted algorithm parameter setting tests and an importance analysis to explore how the algorithm works. We found that the pixel pairs directing along the object structure and with a distance of the approximate object size can generate more discriminative pixel comparison features. Comparison with other benchmark results shows that this algorithm can approach the performance of state-of-the-art deep learning algorithms and exceed them in computational efficiency. We conclude that the proposed algorithm has high potential for urban LiDAR classification.