We present a compressive lens-free technique that performs tomographic imaging across a cubic millimeter-scale volume from highly sparse data. Compared with existing lens-free 3D microscopy systems, our method requires an order of magnitude fewer multi-angle illuminations for tomographic reconstruction, leading to a compact, cost-effective and scanning-free setup with a reduced data acquisition time to enable high-throughput 3D imaging of dynamic biological processes. We apply a fast proximal gradient algorithm with composite regularization to address the ill-posed tomographic inverse problem. Using simulated data, we show that the proposed method can achieve a reconstruction speed ∼10× faster than the state-of-the-art inverse problem approach in 3D lens-free microscopy. We experimentally validate the effectiveness of our method by imaging a resolution test chart and polystyrene beads, demonstrating its capability to resolve micron-size features in both lateral and axial directions. Furthermore, tomographic reconstruction results of neuronspheres and intestinal organoids reveal the potential of this 3D imaging technique for high-resolution and high-throughput biological applications.