Heartbeat detection is one of key techniques to monitor our health condition in daily life, and demands for this technique have increased year and year. Thanks to the non-contact and non-invasive features, various Doppler sensor-based detection methods have been investigated so far. However, the heartbeat detection accuracy of the conventional methods could get degraded due to the low SNR (Signal-to-Noise Ratio) of heartbeat components. Thus, even after some signal processing, non-heartbeat components still remain over such processed signal, which could degrade the heartbeat detection accuracy. In particular for the subjects with low HR (Heart Rate), the estimated HR tends to be higher than the ground truth HR due to such non-heartbeat components, though the conventional methods have mainly focused on the heartbeat detection against the subjects with the normal HR higher than 50 bpm (Beats Per Minute). In this paper, to accurately detect heartbeat even with low HR via a Doppler sensor, we propose a heartbeat detection method based on heartbeat signal reconstruction with convolutional LSTM (Bidirectional-Long Short-Term Memory). In the proposed method, to reconstruct a heartbeat signal based on the periodicity of heartbeat and the spectrum distribution peculiar to heartbeat, successive spectrograms that might be due to heartbeat is used as an input to convolutional LSTM. In addition, for better reconstruction of a heartbeat signal, the previously estimated RRI (R-R Interval) is also used as a feature in the proposed deep learning model with convolutional LSTM. Through the experiments, we confirmed that our proposed method accurately detected heartbeat against 17 subjects including the ones with the HR lower than 50 bpm.