Light Detection and Ranging (LiDAR) technology is now becoming the main tool in many applications such as autonomous driving and human–robot collaboration. Point-cloud-based 3D object detection is becoming popular and widely accepted in the industry and everyday life due to its effectiveness for cameras in challenging environments. In this paper, we present a modular approach to detect, track and classify persons using a 3D LiDAR sensor. It combines multiple principles: a robust implementation for object segmentation, a classifier with local geometric descriptors, and a tracking solution. Moreover, we achieve a real-time solution in a low-performance machine by reducing the number of points to be processed by obtaining and predicting regions of interest via movement detection and motion prediction without any previous knowledge of the environment. Furthermore, our prototype is able to successfully detect and track persons consistently even in challenging cases due to limitations on the sensor field of view or extreme pose changes such as crouching, jumping, and stretching. Lastly, the proposed solution is tested and evaluated in multiple real 3D LiDAR sensor recordings taken in an indoor environment. The results show great potential, with particularly high confidence in positive classifications of the human body as compared to state-of-the-art approaches.