Tracking of low-visibility targets in complex backgrounds is an important research field, where existing methods struggle to image low-visibility targets with irregular changes in moving direction and speed. Move contrast imaging can greatly improve the sensitivity of target tracking, which has achieved important applications in the field of X-ray imaging, including high-resolution imaging to microvessels in living rats with the help of contrast agents, in-situ dynamic observation of ion migration and redox reactions during electrochemical reactions, and water refilling along vessels in willow branch without resorting to agents. However, all these applications are limited to imaging with fixed trajectories or monotonous backgrounds. In principle, move contrast imaging is based on the frequency spectral characteristics of the time-domain grayscale signal and is highly sensitive to moving components, which is wavelength-independent. This paper extends the move contrast imaging to the visible light waveband for tracking free-moving targets in time-varying complex backgrounds. To meet the need for tracking imaging of free-moving targets in complex backgrounds, we develop a move contrast imaging (MCI) method based on continuous wavelet transform (CWT) and Hilbert-Huang transform (HHT) with high discriminatory capability for non-stationary signals. Selecting birds in the sky and forest for the tracking imaging, the irregular grayscale changes caused by natural light intensity in the wild field and random swaying of tree leaves result in complex imaging backgrounds. The tracing results of low-visibility free-moving targets show that FT-MCI method, CWT-MCI method and HHT-MCI method can improve the target tracing imaging sensitivity by 179.9 times, 175.8 times and 214.6 times compared with temporal subtraction imaging, respectively. The results of tracking imaging of free-moving targets in complex backgrounds show that compared with the FT-MCI method and CWT-MCI method, the HHT-MCI method can further effectively suppress the influence of background noise on tracking imaging of targets of interest, thus achieving high sensitivity imaging of free-moving targets in time-varying complex backgrounds. Combining the phase diagram of FT-MCI and the imaging parameters, we can further show the motion direction, the motion speed or the distance from the observation point. Therefore, the HHT-MCI imaging method developed in this paper is expected to provide a novel method for tracking free-moving targets in time-varying complex backgrounds.