A method of manufacturing an electron-emitting source includes first to
third steps. In the first step, a cathode structure made of a metal
containing any one of ion, nickel, cobalt, and chromium is heated to a
first temperature in a reaction furnace to which a carbon source gas has
been introduced, to form a plurality of first carbon nanotubes on the
cathode structure by chemical vapor deposition. In the second step, the
metal serving as a material of the cathode structure is deposited on at
least either one of the cathode structure and the plurality of first
carbon nanotubes, to form a catalyst metal layer. In the third step, the
cathode structure including the catalyst metal layer is heated to a
second temperature higher than the first temperature in the reaction
furnace to which the carbon source gas has been introduced, to form a
plurality of second carbon nanotubes which are thinner than the first
carbon nanotubes on the catalyst metal layer by chemical vapor
deposition. An electron-emitting source is also disclosed.