Millimeter Wave(mmWave) radar is now widely used for vital sign monitoring, and the measurement of physical signs such as heart rate and respiratory rate is achieved by radio signals with non-contact and privacy protection features. To reduce the influence of breathing and its harmonics on heart rate estimation, this paper investigates heart rate monitoring based on frequency modulated continuous wave (FMCW) radar. First, a radar IF signal preprocessing process is established to extract the phase signal for the noise interference problem caused by the surrounding environmental clutter. Then, respiration and heart rate are extracted using a vital sign extraction algorithm based on FMCW phase change and digital filters. Finally, a new heart rate estimation method is implemented by intercepting the time period with a lower rate of respiration-induced thoracic volume change according to the different rates of thoracic undulation change during respiration, and the feasibility of the method is verified by further experiments.