Developing driving safety system with medical assistance devices for preventing accidents has become a major social issue in recent year. These devices have been developed using electrocardiogram (ECG) and photoplethysmogram (PPG) for measuring the heart rate (HR). However, driver should directly contact with the sensor for monitoring the HR. Recently, non-contact system based on continuous-wave Doppler radar has widely studied for monitoring HR. The periodogram by Fast Fourier Transform (FFT) was used for estimating HR. However, if motion artifacts by movement of driver and vehicle vibration contaminate the radar signal, we cannot find spectral peak of HR using FFT. In this paper, we propose a method using multiple signal classification (MUSIC) for estimating HR. We compared MUSIC algorithms with a commonly used FFT method using real experiment data while driving. The results indicate that our proposed method can estimate HR accurately from received radar Doppler signal with motion artifacts.