The object of the present invention is to enable the optical axis of an electron beam of a field emission electron gun mounting thereon an electron gun composed of a fibrous carbon material to be adjusted easily. Moreover, it is also to obtain an electron beam whose energy spread is narrower than that of the electron gun. Further, it is also to provide a high resolution electron beam applied device mounting thereon the field emission electron gun. The means for achieving the objects of the present invention is in that the fibrous carbon material is coated with a material having a band gap, in the field emission electron gun including an electron source composed of a fibrous carbon material and an electrically conductive base material for supporting the fibrous carbon material, an extractor for field-emitting electrons, and an accelerator for accelerating the electrons. Moreover, it is also to apply the field emission electron gun to various kinds of electron beam applied devices.