3D deep learning performance depends on object representation and local feature extraction. In this work, we present MAT-Net, a neural network which captures local and global features from the Medial Axis Transform (MAT). Different from K-Nearest-Neighbor method which extracts local features by a fixed number of neighbors, our MAT-Net exploits effective modules Group-MAT and Edge-Net to process topological structure. Experimental results illustrate that MAT-Net demonstrates competitive or better performance on 3D shape recognition than state-of-the-art methods, and prove that MAT representation has excellent capacity in 3D deep learning, even in the case of low resolution.