A fine hole electric discharge machine includes a machining tank, a storage tank, at least one pipeline, a guide base, a liquid current generator, and a controller. The at least one pipeline has at least one opening directed to the upper surface of a workpiece and allows machining liquid to flow through. The liquid current generator selectively forms a first liquid current in which the machining liquid is supplied from the storage tank and jetted from a predetermined opening of the opening, or a second liquid current in which the machining liquid is sucked from an opening the same as or different from the predetermined opening and recovered to the storage tank. The controller controls the liquid current generator to form the first liquid current or the second liquid current.