This paper describes a non-contact and noise-tolerant heart rate monitoring system using a 24-GHz microwave Doppler sensor. The microwave Doppler sensor placed at some distance from the user's chest detects the small vibrations of the body surface due to the heartbeats. The objective of this work is to detect the instantaneous heart rate (IHR) using this non-contact system in a car, because the possible application of the proposed system is a driver health monitoring based on heart rate variability analysis. IHR can contribute to preventing heart-triggered disasters and to detect mental stress state. However, the Doppler sensor system is very sensitive and it can be easily contaminated by motion artifacts and road noise especially while driving. To address this problem, time-frequency analysis using the parametric method and template matching method are employed. Measurement results show that the Doppler sensor, which is pasted on the clothing surface, can successfully extract the heart rate through clothes. The proposed method achieves 13.1-ms RMS error in IHR measurements conducted on 11 subjects in a car on an ordinary road.