Mm-wave FMCW radar technology for measurement vital signs has great medical value. However, it is an arduous task to realize high-precision heartbeat rate detection for the sake human motion and various interference. This paper proposes a non-contact heartbeat rate detection technique framework based on deep learning to eliminate different interferences. (a) The vital sign signal is pre-processed to exact the phase difference. (b) Heartbeat signals were extracted from the pre-processed signals collected by FMCW radar using Variational Mode Extraction (VME). (c) Different heart rate signals are trained in the Physio Net ECG-ID database using a wavelet scattering network (WSN)-long short-term memory network (LSTM). And the heartbeat signals obtained from the VME decomposition are fed into the training network to determine the heartbeat signal state. The state of the heartbeat signal in turn changes the reference noise of the recursive least squares (RLS) based adaptive filter. (d) Noise, artifacts, and other unwanted signals are filtered out using an adaptive filter. Finally, we perform heart rate estimation on the processed heartbeat signal using Fast Fourier Transform (FFT). This method achieves heart rate detection in different states and is easy to implement. To verify the heart rate detection accuracy of our method, the results are compared with a reliable reference sensor. The results showed that the mean absolute error (MAE) of heart rate of this proposed framework in different states was lower than that of the original method.