We present PU-Refiner, a generative adversarial network for point cloud upsampling. The generator of our network includes a coarse feature expansion module to create coarse upsampled features, a geometry generation module to regress a coarse point cloud from the coarse upsampled features, and a progressive geometry refinement module to restore the dense point cloud in a coarse-to-fine fashion based on the coarse upsampled point cloud. The discriminator of our network helps the generator produce point clouds closer to the target distribution. It makes full use of multi-level features to improve its classification performance. Extensive experimental results show that PU-Refiner is superior to five state-of-the-art point cloud upsampling methods. Code: https://github.com/liuhaoyun/PU-Refiner.