Theory of the light instantaneously emitted by Cherenkov radiation is applied to diagnosing peak current and electron-beam micro-pulse bunch structure of RF-linac. The relativistic electron-beam hitting fused silica generates visible light, which is measured by ps-streak camera. Therefore, parameters of electron-beam micro-pulse can be obtained. This method can diagnose breadth and bunch structure of electron-beam micro-pulse of L-band RF-linac,which makes it possible to form a suit of on-line measurement system of electron-beam micro-pulse of an accelerator.