Falls are a serious health concern and a main cause of injuries among elders living independently at home. In this paper, we describe a new system for real-time automatic fall detection. In contrast to related formulations, the system employs a single continuous-wave micro-Doppler radar sensor to monitor a subject and Long Short-Term Memory based recurrent neural network (RNN) to identify falls from the time-frequency characteristics of the sensor’s returns. It does not require extra hardware or big data set to classify abrupt and slow falls from non-fall actions with superior detection accuracy.