In recent years, with the improvement of computer vision technology, intelligent following robots have also been rapidly developed, greatly improving people's lives. This paper mainly studies the design and implementation of intelligent robot following system considering finite difference method. In this paper, the liDAR sensor, servo motor and control board of the tracking robot system are debugged under the ROS system, and the software and hardware platform of the tracking robot system are built and tested with the modular engineering thinking. The object detection of the following robot system is studied with finite difference method. Through field experiments in complex indoor environment and outdoor corridor, the real-time performance and effectiveness of the robot target following system are verified.