A body motion artifact cancellation (BMAC) technique is proposed to detect human cough signals using a frequency-modulated continuous-wave (FMCW) radar. Human coughs are spontaneously accompanied by large-scale body motions, which overwhelm small-scale vibration signals induced by coughing. To mitigate these effects, motion-induced phase variations are estimated and compensated at respective frequencies of an FMCW signal. The cough signals are extracted from range profiles of the phase-compensated FMCW signals. This allows collecting cough signals at a fixed range bin, which are not so much distorted by range migrations due to the large-scale body motions. It is verified through both simulations and experiments. The experimental result shows that it can clearly detect human cough signals by removing body motion artifacts.