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Point-cloud upsampling aims to generate dense point sets from sparse or incomplete 3D data. Most existing work uses a point-to-point framework. While this method achieves high geometric precision, it is slow because of irregular memory accesses to process unstructured point data. Alternatively, voxel-based methods offer computational efficiency by using regular grids, but struggle to preserve precise point locations due to discretization. To resolve this efficiency-precision trade-off, we introduce Hybrid Voxels, a representation that combines both voxel occupancy and a continuous point offset. We then present the Hybrid-Voxel Point-cloud Upsampling Network (HVPUNet), an efficient framework built upon this representation. HVPUNet integrates two key modules: (1) Shape Completion to restore missing geometry by filling empty voxels, and (2) Super-Resolution to enhance spatial resolution and capture finer surface details. We also use progressive refinement, operational voxel expansion, and implicit geometric learning. Experimental results demonstrate that HVPUNet can upsample point clouds at significantly lower computational cost than the state-of-the-art, but with comparable model accuracy.