Due to the development of short-range radar with high-resolution, the radar sensor has a high potential to be used in real human-computer interaction (HCI) applications. The radar sensor has advantages over optical cameras in that it is unaffected by illumination and it is able to detect the objects in an occluded environment. This paper proposes a hand gesture recognition system for a real-time application of HCI using 60 GHz frequency-modulated continuous wave (FMCW) radar, Soli, developed by Google. The overall system includes signal processing part that generates range-Doppler map (RDM) sequences without clutter and machine learning part including a long short-term memory (LSTM) encoder to learn the temporal characteristics of the RDM sequences. A set of data is collected from 10 participants for the experiment. The proposed hand gesture recognition system successfully distinguishes 10 gestures with a high classification accuracy of 99.10%. It also recognizes the gestures of a new participant with an accuracy of 98.48%.