Point clouds acquired from 3D sensors are usually sparse and noisy. Point cloud upsampling is an approach to increase the density of the point cloud so that detailed geometric information can be restored. In this paper, we propose a Dual Back-Projection network for point cloud upsampling (DBPnet). A Dual Back-Projection is formulated in an up-down-up manner for point cloud upsampling. It not only back projects feature residues but also coordinates residues so that the network better captures the point correlations in the feature and space domains, achieving lower reconstruction errors on both uniform and non-uniform sparse point clouds. Our proposed method is also generalizable for arbitrary upsampling tasks (e.g. 4x, 5.5x). Experimental results show that the proposed method achieves the lowest point set matching losses with respect to the benchmark. In addition, the success of our approach demonstrates that generative networks are not necessarily needed for non-uniform point clouds.