In this Letter, we present a significant improvement to time and space resolutions in electro-optic sampling (EO) for two-dimensional terahertz (THz) near-field imaging. Using a THz microscope, we readapt a recent EO sampling scheme based on optical probe spectrum filtering. Combined with an ultra-thin EO crystal, we achieve record broadband video-rate THz near-field imaging. Particularly, this new scheme improves the THz bandwidth, the imaging contrast, and the spatial resolution. To validate our method, we show THz near-field images ranging from 100 GHz to 4 THz with a spatial resolution up to λ/600 at 100 GHz. This demonstration positively affects the detection of intense THz pulses derived from the tilted-pulse-front excitation of lithium niobate and will accelerate our understanding of the interaction processes between electromagnetic waves and the conducting electrons of metallic interfaces.