Drone detection in FMCW radar system needs complex techniques because a drone beat frequency is highly dynamic and unpredictable. Therefore, the current static signal processing algorithms cannot show appropriate detection accuracy. With dynamic signal fluctuation and environmental clutters, it can fail to detect a drone or make false detection. It affects to the radar system integrity and safety. Constant false alarm rate (CFAR), one of famous static signal process algorithm is effective for static environment. But for drone detection, it shows low detection accuracy. In this paper, we suggest neural network based FMCW radar system for detecting a drone. We use recurrent neural network (RNN) because it is the effective neural network for signal processing. In our FMCW radar system, one transmitter emits FMCW signal and four-way fixed receivers detect reflected drone beat frequency. The coordinate of the drone can be calculated with four receivers information by triangulation. Therefore, RNN only learns and inferences reflected drone beat frequency. It helps higher learning and detection accuracy. With several drone flight experiments, RNN shows false detection rate and detection accuracy as 21.1% and 96.4%, respectively.