In this paper, feature-based gesture recognition in a frequency modulated continuous wave (FMCW) radar system is introduced. We obtain a range-Doppler map (RDM) from raw signals of FMCW radar and generate a variety of features from the RDM. The features are broadly defined to reflect radar-specific characteristics as well as statistical values commonly used in machine learning. Among these radar features, those that are highly correlated with gesture recognition are selected by the proposed feature selection algorithm, which is a wrapper-based feature selection algorithm incorporated with a quantum-inspired evolutionary algorithm (QEA). Furthermore, the information factor based on the minimum redundancy maximum relevance criterion is applied to QEA in order to find feature subsets effectively. The proposed algorithm is able to extract from all feature sets feature subsets related to gesture recognition, and improves the gesture recognition accuracy of the FMCW radar system. In addition, we analyze which features of the radar are helpful for gesture recognition and perform effective gesture recognition using the features determined through feature analysis.