A 24-GHz radar system for biomedical applications is designed, fabricated, and tested. The proposed radar system includes a flexible radio frequency (RF) board and a rigid baseband board. The RF board integrates two 4×4 patch arrays, a voltage controlled oscillator (VCO), two low noise amplifiers (LNA), and a six-port structure. The baseband board has baseband amplifiers as well as an on-board sawtooth voltage generator (SVG). The SVG generates a 155-Hz sawtooth voltage signal to control the VCO. A 450-MHz bandwidth frequency ramp with a center frequency around 24 GHz is transmitted. With the proposed radar system, the inverse synthetic aperture radar (ISAR) imaging method is used to track moving targets in a crowded environment with stationary clutter. The theory of ISAR imaging is detailed in this paper. Two experiments were carried out to reveal the capabilities of the radar system in tracking single and multiple moving targets. The radar system is featured as being flexible and portable. The complete radar system has overall dimensions of 118mm×45mm×15mm.