In this paper, a sparsity-driven method of micro-Doppler analysis is proposed for dynamic hand gesture recognition with radar sensors. First, sparse representations of the echoes reflected from dynamic hand gestures are achieved through the Gaussian-windowed Fourier dictionary. Second, the micro-Doppler features of dynamic hand gestures are extracted using the orthogonal matching pursuit algorithm. Finally, the nearest neighbor classifier is combined with the modified Hausdorff distance to recognize dynamic hand gestures based on the sparse micro-Doppler features. Experiments with real radar data show that the recognition accuracy produced by the proposed method exceeds 96% under moderate noise, and the proposed method outperforms the approaches based on principal component analysis and deep convolutional neural network with small training dataset.