A 790-nm-driven high-harmonic generation source with a repetition rate of 6 kHz is combined with a toroidal-grating monochromator and a high-detection-efficiency photoelectron time-of-flight momentum microscope to enable time- and momentum-resolved photoemission spectroscopy over a spectral range of 23.6-45.5 eV with sub-100 fs time resolution. Three-dimensional (3D) Fermi surface mapping is demonstrated on graphene-covered Ir(111) with energy and momentum resolutions of ≲100 meV and ≲0.1 Å-1, respectively. The tabletop experiment sets the stage for measuring the kz-dependent ultrafast dynamics of 3D electronic structure, including band structure, Fermi surface, and carrier dynamics in 3D materials as well as 3D orbital dynamics in molecular layers.