A space-based Very Long Baseline Interferometry (VLBI) program, named as the Cosmic Microscope, is proposed to involve dual VLBI telescopes in the space working together with giant ground-based telescopes (e.g., Square Kilometre Array, FAST, Arecibo) to image the low radio frequency Universe with the purpose of unraveling the compact structure of cosmic constituents including supermassive black holes and binaries, pulsars, astronomical masers and the underlying source, and exoplanets amongst others. The operational frequency bands are 30, 74, 330 and 1670 MHz, supporting broad science areas. The mission plans to launch two 30-m-diameter radio telescopes into 2 000 km×90 000 km elliptical orbits. The two telescopes can work in flexibly diverse modes. (i) Space-ground VLBI. The maximum space-ground baseline length is about 100 000 km; it provides a high-dynamic-range imaging capacity with unprecedented high resolutions at low frequencies (0.3 mas at 1.67 GHz and 20 mas at 30 MHz) enabling studies of exoplanets and supermassive black hole binaries (which emit nanoHz gravitational waves). (ii) Space-space single-baseline VLBI. This unique baseline enables the detection of flaring hydroxyl masers, and more precise position measurement of pulsars and radio transients at mas level. (iii) Single dish mode, where each telescope can be used to monitor transient bursts and rapidly trigger follow-up VLBI observations. The large space telescope will also contribute in measuring and constraining the total angular power spectrum from the Epoch of Reionization. In short, the Cosmic Microscope offers astronomers the opportunity to conduct novel, frontier science.