A cathode substrate 10 is heated to 400 to 600° 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.