Recently deep learning has achieved significant progress on point cloud analysis tasks. Learning good representations is of vital importance to these tasks. Most current methods rely on massive labelled data for training. We here propose a point discriminative learning method for unsupervised representation learning on 3D point clouds, which can learn local and global geometry features. We achieve this by imposing a novel point discrimination loss on the middle level and global level point features produced in the backbone network. This point discrimination loss enforces the features to be consistent with points belonging to the shape surface and inconsistent with randomly sampled noisy points. Our method is simple in design, which works by adding an extra adaptation module and a point consistency module for unsupervised training of the encoder in the backbone network. Once trained, these two modules can be discarded during supervised training of the classifier or decoder for down-stream tasks. We conduct extensive experiments on 3D object classification, 3D part segmentation and shape reconstruction in various unsupervised and transfer settings. Both quantitative and qualitative results show that our method learns powerful representations and achieves new state-of-the-art performance.