A field-emission electron gun includes a field-emission cathode including a single fiber-like carbon substance and an electrically-conductive substrate for supporting the substance, an extractor for field-emitting electrons, an accelerating electrode for accelerating the electrons, an extracting power-supply for applying extracting voltage to the extractor, an accelerating power-supply for applying accelerating voltage to the accelerating electrode, and a unit for detecting and monitoring a part of emission current. In this field-emission electron gun, if emission-variation amount has become larger than a predetermined value, the extracting voltage is automatically boosted for a constant length of time, thereby increasing the emission current up to a predetermined value. Further, extracting voltage at the time of boosting the extracting voltage, voltage-boosting time, and the emission current are recorded, then being feed-backed to voltage-boosting conditions for the next-time extracting voltage. Moreover, the accelerating voltage is varied in correspondence with the voltage-boosting of the extracting voltage.