Automatic classification of light detection and ranging (LiDAR) data in urban areas is of great importance for many applications such as generating three-dimensional (3D) building models and monitoring power lines. Traditional supervised classification methods require training samples of all classes to construct a reliable classifier. However, complete training samples are normally hard and costly to collect, and a common circumstance is that only training samples for a class of interest are available, in which traditional supervised classification methods may be inappropriate. In this study, we investigated the possibility of using a novel one-class classification algorithm, i.e., the presence and background learning (PBL) algorithm, to classify LiDAR data in an urban scenario. The results demonstrated that the PBL algorithm implemented by back propagation (BP) neural network (PBL-BP) could effectively classify a single class (e.g., building, tree, terrain, power line, and others) from airborne LiDAR point cloud with very high accuracy. The mean F-score for all of the classes from the PBL-BP classification results was 0.94, which was higher than those from one-class support vector machine (SVM), biased SVM, and maximum entropy methods (0.68, 0.82 and 0.93, respectively). Moreover, the PBL-BP algorithm yielded a comparable overall accuracy to the multi-class SVM method. Therefore, this method is very promising in the classification of the LiDAR point cloud.