Point set is a major type of 3D structure representation format characterized by its data availability and compactness. Most former deep learning-based point set models pay equal attention to different point set regions and channels, thus having limited ability in focusing on small regions and specific channels that are important for characterizing the object of interest. In this paper, we introduce a novel model named Attention-based Point Network (AttPNet). It uses attention mechanism for both global feature masking and channel weighting to focus on characteristic regions and channels. There are two branches in our model. The first branch calculates an attention mask for every point. The second branch uses convolution layers to abstract global features from point sets, where channel attention block is adapted to focus on important channels. Evaluations on the ModelNet40 benchmark dataset show that our model outperforms the existing best model in classification tasks by 0.7% without voting. In addition, experiments on augmented data demonstrate that our model is robust to rotational perturbations and missing points. We also design a Electron Cryo-Tomography (ECT) point cloud dataset and further demonstrate our model’s ability in dealing with fine-grained structures on the ECT dataset.