Aiming at the problems of low echo signal-to-noise ratio, large amount of data, and weak interpretability of features in radar micro-motion gesture recognition, a micro-motion gesture recognition system using an ultra-wideband radar based on random forest is proposed. The small radar cross section of the micro-motion gesture causes problems such as low signal-to-noise ratio and blurred positive features. As for these problems, the clustering algorithm is used to extract the main vector of echo and construct polynomial features to reduce redundant data and improve the signal-to-noise ratio of gesture echo signals. For the destruction of interpretability during training process of feature maps, random forest is used to visualize the feature contribution rate and select features for applying to the model. Experimental results show that the algorithm has better recognition performance than other algorithms under echo signals with different noise floors, which verifies the effectiveness of the algorithm.