We introduce Airy-beam tomographic microscopy (ATM) for high-resolution, volumetric, inertia-free imaging of biological specimens. The work exploits the highly adjustable Airy trajectories in the three-dimensional (3D) space, transforming the conventional telecentric wide-field imaging scheme that requires sample or focal-plane scanning to acquire 3D information. The results present a consistent near-diffraction-limited 3D resolution across a tenfold extended imaging depth compared to wide-field microscopy. We anticipate the strategy to not only offer a promising paradigm for 3D optical microscopy, but also be translated to other non-optical waveforms.