A cathode substrate 10 is heated to 400 to 600.degree. C. in the
atmosphere of hydrocarbon gas such as methane and the gas is allowed to
react with the surface of the cathode substrate 10 by a thermal CVD
method. Thus, an electron emission source in which graphite nano-fibers
11 are allowed to grow in a gaseous-phase on the surface of the cathode
substrate 10 by using nickel or iron existing on the surface of the
cathode substrate 10 as a nucleus is held between upper and lower end
hats 12 to form a cathode part 13.