Foreign object debris (FOD) denotes any unwanted objects on an airport runway, which must be removed before aircraft take off or land. Millimeter-wave (mm-wave) radar is widely utilized to locate small FODs due to its high-range resolution. However, the main difficulty faced by mm-wave radar is to detect stationary little FODs in heavy ground clutter. We propose a layered FOD detection algorithm using clutter map constant false alarm rate (CFAR) and fractional Fourier transform (FrFT) for a mm-wave radar system working at 77 GHz. In the first stage, we utilized the traditional clutter map CFAR to suppress ground clutter while FOD returns and some false alarms were detected using an adaptive threshold. Then, we propose an FrFT-based pattern classification method to distinguish FODs and false alarms, where a two-dimensional feature vector is extracted and a one-class minimax probability machine classifier is trained to accomplish FOD and false alarm classification. Finally, the effectiveness of the proposed method is verified using some measured data obtained via the 77-GHz mm-wave radar.