Electrocardiography (ECG) is a mandatory standard for monitoring electrical activity of the heart in many clinical settings such as intensive care and emergency units. However, in situations wherein the skin is damaged, such as acute burn injuries, it is impossible to efficiently attach electrodes to the skin. In this study, we developed a non-contact cardiac monitoring system using a 24-GHz medical radar for directly measuring the beat-to-beat heart mechanical activity at a distance from a subject. The heart rate variability (HRV) was analysed using an autoregressive model (AR) from the measured beat-to-beat intervals during a head-up tilt test. To investigate the feasibility of the proposed system, we compared medical radar and ECG recording by using Lin\'s correlation coefficient and Bland-Altman analysis, which showed a negligible mean difference from the substantial agreement of Lin\'s correlation coefficient of 0.9 between the radar and ECG. The non-contact radar clearly monitored dynamic changes in HRV indices induced by the head-up tilt test. This type of non-contact HRV-sensing technique as an alternative approach has significant potential for advancing personal healthcare in both clinical and out-of-hospital settings.