The electrical prebreakdown currents in liquid and solid dielectrics under a highly nonuniform electric field condition have been measured successfully using an electro‐optical current measuring system in conjunction with a 760‐ns rectangular high‐voltage pulse generator. The breakdown time lag was precisely measured from the current. The discharge propagation velocity was estimated from the linear relation to formative time lag and gap spacing to be 18 km/s in liquid nitrogen at +40‐kV point voltage.