To alleviate the shortage of health care workers under the novel coronavirus pneumonia (COVID-19) and to achieve intelligent monitoring of inpatients, this paper proposes a new behavior recognition method based on enhanced micro-Doppler spectrograms in the space-time domain using frequency modulated continuous wave (FMCW) radar. Firstly, constructing a micro-Doppler spectrum of the human behavior acquired by the radar. Then, a new time-space domain enhancement algorithm combining histogram equalization and homomorphic filtering is used for the enhancement of spectrogram information. Finally, an improved convolutional long short term memory network (ConvLSTM) is proposed to extract the time and space features of the spectrum, which effectively identifies seven common inpatient behaviors, such as drinking and falling. The experimental results show that the method in this paper can effectively monitor the patient's behavior, and the recognition accuracy of the seven actions can reach 94%.