Target tracking has found important applications in particle tracking, vehicle navigation, aircraft monitoring, etc. However, employing single-pixel imaging techniques to track a fast-moving object with a high frame rate is still a challenge, due to the limitation of the modulation frequency of the spatial light modulator and the number of required patterns. Here we report a complementary single-pixel object tracking approach which requires only two geometric moment patterns to modulate the reflected light from a moving object in one frame. Using the complementary nature of a digital micromirror device (DMD), two identical single-pixel detectors are used to measure four intensities which can be used to acquire the values of zero-order and first-order geometric moments to track the centroid of a fast-moving object. We experimentally demonstrate that the proposed method successfully tracks a fast-moving object with a frame rate of up to 11.1 kHz in the first two experiments. In the third experiment, we compare previous works and find that the method can also accurately track a fast-moving object with a changing size and moving speed of 41.8 kilopixel/s on the image plane. The root mean squared errors in the transverse and axial directions are 0.3636 and 0.3640 pixels, respectively. The proposed method could be suitable for ultrafast target tracking.