This paper investigates the application of millimeter-wave (mmWave) radar for the estimation of human vital signs. Aiming to obtain more accurate frequency estimation for periodic signals of respiration and heartbeat, we propose the harmonic MUSIC (HMUSIC) algorithm to consider harmonic components for frequency estimation of vital sign signals. In the experiments, we tested different subjects' vital signs. Experimental results demonstrate that the 89-th percentile errors in respiration rate and the 88-th percentile errors in heartbeat rate are less than 3 respirations per minute and 5 beats per minute.