The non-contact heart rate estimation method based on FMCW radar has the advantages of comfort and convenience. Due to the interference of noise and respiratory harmonics, the accuracy of current methods is still limited. To solve this problem, this paper proposes a heart rate estimation method. On the basis of phase analysis, the phase difference operation is performed on the phase signal, which can enhance the heartbeat signal. Then, an improved wavelet threshold denoising method is used for denoising to eliminate noise interference. During frequency estimation, this paper processes the heartbeat signal with the Hamming window function, and then uses the multiple signal classification (MUSIC) algorithm for frequency estimation, which may solve the spectral leakage problem caused by signal interception, and improve the resolution and stability of MUSIC. Thus, the influence of respiratory harmonics and noise on heart rate estimation may be reduced, and accurate heart rate values may be obtained. Simulation results show that the accuracy of heart rate estimation is improved.