Domain Adaptation (DA) approaches achieved significant improvements in a wide range of machine learning and computer vision tasks (i.e., classification, detection, and segmentation). However, as far as we are aware, there are few methods yet to achieve domain adaptation directly on 3D point cloud data. The unique challenge of point cloud data lies in its abundant spatial geometric information, and the semantics of the whole object is contributed by including regional geometric structures. Specifically, most general-purpose DA methods that struggle for global feature alignment and ignore local geometric information are not suitable for 3D domain alignment. In this paper, we propose a novel 3D Domain Adaptation Network for point cloud data (PointDAN). PointDAN jointly aligns the global and local features in multi-level. For local alignment, we propose Self-Adaptive (SA) node module with an adjusted receptive field to model the discriminative local structures for aligning domains. To represent hierarchically scaled features, node-attention module is further introduced to weight the relationship of SA nodes across objects and domains. For global alignment, an adversarial-training strategy is employed to learn and align global features across domains. Since there is no common evaluation benchmark for 3D point cloud DA scenario, we build a general benchmark (i.e., PointDA-10) extracted from three popular 3D object/scene datasets (i.e., ModelNet, ShapeNet and ScanNet) for cross-domain 3D objects classification fashion. Extensive experiments on PointDA-10 illustrate the superiority of our model over the state-of-the-art general-purpose DA methods.