A key challenge when imaging whole biomedical specimens is how to quickly obtain massive cellular information over a large field of view (FOV). We report a subvoxel light-sheet microscopy (SLSM) method enabling high-throughput volumetric imaging of mesoscale specimens at cellular resolution. A nonaxial, continuous scanning strategy is developed to rapidly acquire a stack of large-FOV images with three-dimensional (3-D) nanoscale shifts encoded. Then, by adopting a subvoxel-resolving procedure, the SLSM method models these low-resolution, cross-correlated images in the spatial domain and can iteratively recover a 3-D image with improved resolution throughout the sample. This technique can surpass the optical limit of a conventional light-sheet microscope by more than three times, with high acquisition speeds of gigavoxels per minute. By fast reconstruction of 3-D cultured cells, intact organs, and live embryos, SLSM method presents a convenient way to circumvent the trade-off between mapping large-scale tissue (>100 mm³) and observing single cell (∼1-μm resolution). It also eliminates the need of complicated mechanical stitching or modulated illumination, using a simple light-sheet setup and fast graphics processing unit-based computation to achieve high-throughput, high-resolution 3-D microscopy, which could be tailored for a wide range of biomedical applications in pathology, histology, neuroscience, etc.