We demonstrate an accurate remote measurement of heartbeats using an ultra-wideband radar system. Although most conventional systems use either continuous waves or impulse-radio systems for remote vital monitoring, continuous waves suffer from non-stationary clutters, while impulse-radio systems cannot detect heartbeats. Our ultra-wideband radar system has a moderate fractional bandwidth intermediate of these systems, resulting in both the suppression of clutters and high sensitivity in measuring accurate heart rates even in a dynamic environment. A simultaneous measurement of the vital signal of a participant employing the ultra-wideband radar and electrocardiography reveals the high accuracy of the radar system in measuring the heart rate varying over time.