Two-photon light-sheet fluorescence microscopy enables high-resolution imaging of transient activity in deep tissue at a high frame rate. Traditionally, light-sheet microscopy builds up a 3D stack by multiple sequential depth scans, which significantly limit the volumetric imaging speed. We introduce the depth random-access light-sheet microscopy, allowing rapid switching scanning depth for light-sheet imaging. With a low-cost electrically tunable lens and minimum modification of an existing two-photon light-sheet imaging instrument, we demonstrated fast random depth hopping light-sheet imaging at 100 frames per second in the live brain slice. Through depth random-access, calcium activities for an astrocyte were recorded on four selective detection planes at a refreshing rate of 25 Hz.