According to the X-ray generating apparatus of this invention, a potential corresponding to that of a housing is applied to a first electrode, closest to a cathode, of at least two intermediate electrodes arranged between the cathode and a target. Therefore, even if the first electrode with an increased thermal capacity contacts the housing, the function of the X-ray generating apparatus will never be impaired. As a result, the first electrode is not easily restricted by structure, so that the first electrode may be enlarged as a measure for heat radiation, or that the first electrode may be placed in contact with the housing. The first electrode contacting the housing determines a positional relationship of the electron gun and housing to facilitate assembly of the X-ray generating apparatus. Further, all the potentials of the cathode, intermediate electrodes (e.g. a second electrode and a third electrode) and target will have straight polarity with respect to the potential of the first electrode, which facilitates power source control.