An electron beam generator device includes a base body having a conductive surface and a electron-emission electrode having a carbon nanotube structure on the conductive surface of the substrate. The carbon nanotube structure constitutes a network structure which has plural carbon nanotubes and a crosslinked part including a chemical bond of plural functional groups. The chemical bond connects one end of one of the carbon nanotubes to another one of the carbon nanotubes.A method for producing an electron beam generator device, includes applying plural carbon nanotubes each having a functional group onto a conductive surface of a base body, and crosslinking the functional groups with a chemical bond to form a crosslinked part, thereby forming a carbon nanotube structure constituting a network structure having plural carbon nanotubes electrically connected to each other.