The non-contact measurement of the respiration rate (RR) and heart rate (HR) using a Doppler radar has attracted more attention in the field of home healthcare monitoring, due to the extremely low burden on patients, unconsciousness and unconstraint. Most of the previous studies have performed the frequency-domain analysis of radar signals to detect the respiration and heartbeat frequency. However, these procedures required long period time (approximately 30 s) windows to obtain a high-resolution spectrum. In this study, we propose a time-domain peak detection algorithm for the fast acquisition of the RR and HR within a breathing cycle (approximately 5 s), including inhalation and exhalation. Signal pre-processing using an analog band-pass filter (BPF) that extracts respiration and heartbeat signals was performed. Thereafter, the HR and RR were calculated using a peak position detection method, which was carried out via LABVIEW. To evaluate the measurement accuracy, we measured the HR and RR of seven subjects in the laboratory. As a reference of HR and RR, the persons wore contact sensors i.e., an electrocardiograph (ECG) and a respiration band. The time domain peak-detection algorithm, based on the Doppler radar, exhibited a significant correlation coefficient of HR of 0.92 and a correlation coefficient of RR of 0.99, between the ECG and respiration band, respectively.