Vavilov-Cherenkov radiation, usually just Cherenkov radiation (CR), is commonly used in high energy charged particle and cosmic rays detectors. We have studied CR emitted from very low refractive index material such as silica-aerogel and found it may be useful tool for electron beam diagnostics since the opening angle (Cherenkov angle) is small, then the CR can be transported onto a detector located far from the radiator. We have prepared a thin (1 mm thick) hydrophobic silica-aerogel having refractive index of 1.05 that has been developed at Chiba University. Since the intensity of CR is much stronger than that of optical transition radiation, the CR is a better light source for low intensity beam diagnostics. In order to apply the CR to measurement of bunch length of electron beams, we have investigated properties of CR by numerical simulation study based on the Liénard-Wiechert potentials. In addition, possibility of intense THz source is also discussed.