Conventional millimeter-wave (mm-wave) security screening systems with synthetic or phased arrays require either mechanical or electronic scans which are slow, thus not capable to image on-the-move objects. This article presents the 4-D imaging of on-the-move objects (1-D velocity and 3-D profile) by leveraging cost-effective compressive reflector antennas (CRAs) and software-defined mm-wave (SDMMW) multiple-in multiple-out (MIMO) arrays. The CRA creates spatial aperture coding to achieve informative measurements and high sensing capacity. The SDMMW MIMO array generates fast space-time-coded frequency-modulated continuous wave (FMCW) for quick data collection and simultaneous MIMO operation. The signal model using the CRAs fed by the SDMMW MIMO arrays in a multistatic configuration is derived, followed by the sensing-matrix-based imaging theory. Then, a proof-of-concept imaging system is designed with a made-in-lab CRA and a modularized 8-by-8 SDMMW array where the fast FMCW modulation achieves a linearized frequency sweep of 5.02 GHz per 50 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mu }\text{s}$ </tex-math></inline-formula> , corresponding to a high data acquisition rate of 2500 volumetric frames/s and an unambiguous velocity of ±2.23 m/s. Both simulations and experiments have shown good imaging performance of on-the-move objects, giving great potential for developing future cost-effective high-throughput mm-wave security screening systems.