A microhole electric discharge machining apparatus that forms a conical inverse-tapered hole on a workpiece by a thin wire electrode, includes, an electrode holder that holds an upper part of the thin wire electrode and feeds a lower part of the thin wire electrode downward to stretch the lower part to the workpiece by rotating the thin wire electrode; a first guide member that is arranged near the workpiece upper surface and is provided with a first guide hole through which the thin wire electrode is penetrated on a hole-machining axis; a second guide member that is arranged between the first guide member and the electrode holder and is provided with a second guide hole through which the thin wire electrode is penetrated at a position eccentric from the hole-machining axis; and a swivel driving unit that circularly swivels the second guide member around the hole-machining axis.