Volumetric interrogation of the organization and processes of intracellular organelles and molecules in cellular systems with a high spatiotemporal resolution is essential for understanding cell physiology, development, and pathology. Here, we report high-resolution Fourier light-field microscopy (HR-FLFM) for fast and volumetric live-cell imaging. HR-FLFM transforms conventional cell microscopy and enables exploration of less accessible spatiotemporal-limiting regimes for single-cell studies. The results present a near-diffraction-limited resolution in all three dimensions, a five-fold extended focal depth to several micrometers, and a scanning-free volume acquisition time up to milliseconds. The system demonstrates instrumentation accessibility, low photo damage for continuous observation, and high compatibility with general cell assays. We anticipate HR-FLFM to offer a promising methodological pathway for investigating a wide range of intracellular processes and functions with exquisite spatiotemporal contextual details.