This paper presents a variational mode decomposition (VMD)-based heart rate extraction algorithm to extract heart rate of the target under intermittent interference of non-stationary clutters caused by another person. When nonstationary clutters exist around the interested target, the heart rate detection becomes difficult for FMCW radars. In regard to the situation, VMD is utilized to extract the heartbeat signal and suppress the effect of non-stationary clutters after applying filter preprocessing. This approach is compared to other methods based on ensemble empirical mode decomposition (EEMD) and traditional fast Fourier transform (FFT). As a result, the proposed algorithm can achieve low computational load and high accuracy of heart rate extraction with relative error of 1.7%. The heartbeat signal extracted by the proposed algorithm has signal-to-noise ratio (SNR) improvement of 2.4 dB compared with EEMD algorithm.