Imaging systems with miniaturized device footprint, real-time processing speed and high resolution three-dimensional (3D) visualization are critical to broad biomedical applications such as endoscopy. Most of existing imaging systems rely on bulky lenses and mechanically refocusing to perform 3D imaging. Here, we demonstrate GEOMScope, a lensless single-shot 3D microscope that forms image through a single layer of thin microlens array and reconstructs objects through an innovative algorithm combining geometrical-optics-based pixel back projection and background suppressions. We verify the effectiveness of GEOMScope on resolution target, fluorescent particles and volumetric objects. Comparing to other widefield lensless imaging devices, we significantly reduce the required computational resource and increase the reconstruction speed by orders of magnitude. This enables us to image and recover large volume 3D object in high resolution with near real-time processing speed. Such a low computational complexity is attributed to the joint design of imaging optics and reconstruction algorithms, and a joint application of geometrical optics and machine learning in the 3D reconstruction. More broadly, the excellent performance of GEOMScope in imaging resolution, volume, and reconstruction speed implicates that geometrical optics could greatly benefit and play an important role in computational imaging.