Vital signs such as heart rate and respiration rate are among the most important physiological signals for health monitoring and medical applications. Impulse radio (IR) ultra-wideband (UWB) radar becomes one of the essential sensors in non-contact vital signs detection. The heart pulse wave is easily corrupted by noise and respiration activity since the heartbeat signal has less power compared with the breathing signal and its harmonics. In this paper, a signal processing technique for a UWB radar system was developed to detect the heart rate and respiration rate. There are four main stages of signal processing: (1) clutter removal to reduce the static random noise from the environment; (2) independent component analysis (ICA) to do dimension reduction and remove noise; (3) using low-pass and high-pass filters to eliminate the out of band noise; (4) modified covariance method for spectrum estimation. Furthermore, higher harmonics of heart rate were used to estimate heart rate and minimize respiration interference. The experiments in this article contain different scenarios including bed angle, body position, as well as interference from the visitor near the bed and away from the bed. The results were compared with the ECG sensor and respiration belt. The average mean absolute error (MAE) of heart rate results is 1.32 for the proposed algorithm.