Reconstructing a high-resolution 3D model of an object is a challenging task in computer vision. Designing scalable and light-weight architectures is crucial while addressing this problem. Existing point-cloud based reconstruction approaches directly predict the entire point cloud in a single stage. Although this technique can handle low-resolution point clouds, it is not a viable solution for generating dense, high-resolution outputs. In this work, we introduce DensePCR, a deep pyramidal network for point cloud reconstruction that hierarchically predicts point clouds of increasing resolution. Towards this end, we propose an architecture that first predicts a low-resolution point cloud, and then hierarchically increases the resolution by aggregating local and global point features to deform a grid. Our method generates point clouds that are accurate, uniform and dense. Through extensive quantitative and qualitative evaluation on synthetic and real datasets, we demonstrate that DensePCR outperforms the existing state-of-the-art point cloud reconstruction works, while also providing a light-weight and scalable architecture for predicting high-resolution outputs.