Microwave photonic radars enable fast or even real-time high-resolution imaging thanks to its broad bandwidth. Nevertheless, the frequency range of the radars usually overlaps with other existed radio-frequency (RF) applications, and only a centimeter-level imaging resolution has been reported, making them insufficient for civilian applications. Here, we propose a microwave photonic imaging radar with a millimeter-level resolution by introducing a frequency-stepped chirp signal based on an optical frequency shifting loop. As compared with the conventional linear-frequency modulated (LFM) signal, the frequency-stepped chirp signal can bring the system excellent capability of anti-interference. In an experiment, a frequency-stepped chirp signal with a total bandwidth of 18.2 GHz (16.9 to 35.1 GHz) is generated. Postprocessing the radar echo, radar imaging with a two-dimensional imaging resolution of ~8.5 mm$\times$~8.3 mm is achieved. An auto-regressive algorithm is used to reconstruct the disturbed signal when a frequency interference exists, and the high-resolution imaging is sustained.