Accurate recognition of fine-grained gestures is a prerequisite for their application in emerging scenarios, such as smart cars and smart phones. In this paper, we propose a novel neural network based strategy to identify the range, doppler, and angle features inherent in gestures acquired by millimeter-wave frequency-modulated continuous wave (FMCW) radar. First, a dataset with eight different fine-grained gestures is created, where the gesture signals are echoes after dechirping. Since the raw data is difficult to process directly, range, angle and doppler features of fine-grained gestures are extracted with high resolution by using Multiple Signal Classification (MUSIC) algorithm, Short-Time Fourier Transform (STFT), respectively. Particularly, we design an improved Deep Residual Shrinkage Network (DRSN) with variable channels to recognize features of fine-grained gestures. Experiments validate the effectiveness of the proposed architecture, and an impressive accuracy of 98.8% is achieved in the triple-channel network structure.