Real-time tracking of fast-moving object have many important applications in various fields. However, it is a great challenge to track of fast-moving object with high frame rate in real-time by employing single-pixel imaging technique. In this paper, we present the first single-pixel imaging technique that measures zero-order and first-order geometric moments, which are leveraged to reconstruct and track the centroid of a fast-moving object in real time. This method requires only 3 geometric moment patterns to illuminate a moving object in one frame. And the corresponding intensities collected by a single-pixel detector are equivalent to the values of the zero-order and first-order geometric moments. We apply this new approach of measuring geometric moments to object tracking by detecting the centroid of the object in two experiments. The root mean squared errors in the transverse and axial directions are 5.46 pixels and 5.53 pixels respectively, according to the comparison of data captured by a camera system. In the second experiment, we successfully track a moving magnet with a frame rate up to 7400 Hz. The proposed scheme provides a new method for ultrafast target tracking applications.