High-speed visualization of three-dimensional (3D) processes across a large field of view with cellular resolution is essential for understanding living systems. Light-field microscopy (LFM) has emerged as a powerful tool for fast volumetric imaging. However, one inherent limitation of LFM is that the achievable lateral resolution degrades rapidly with the increase of the distance from the focal plane, which hinders the applications in observing thick samples. Here, we propose Spherical-Aberration-assisted scanning LFM (SAsLFM), a hardware-modification-free method that modulates the phase-space point-spread-functions (PSFs) to extend the effective high-resolution range along the z-axis by ~ 3 times. By transferring the foci to different depths, we take full advantage of the redundant light-field data to preserve finer details over an extended depth range and reduce artifacts near the original focal plane. Experiments on a USAF-resolution chart and zebrafish vasculatures were conducted to verify the effectiveness of the method. We further investigated the capability of SAsLFM in dynamic samples by imaging large-scale calcium transients in the mouse brain, tracking freely-moving jellyfish, and recording the development of Drosophila embryos. In addition, combined with deep-learning approaches, we accelerated the three-dimensional reconstruction of SAsLFM by three orders of magnitude. Our method is compatible with various phase-space imaging techniques without increasing system complexity and can facilitate high-speed large-scale volumetric imaging in thick samples.