To provide a field-emission display element using a perpendicularly oriented carbon nanotube.

On a lower substrate 30, a first metal film 32 for cathode electrode is formed and then a carbon nanotube 34 thereon. A first spacer 36 has been provided on the first metal film 32, and a meshwork of the second metal film 38 used as gate electrode is supported above the carbon nanotube 34. Provided on the first spacer 36 is a second spacer 49, on which an upper substrate 50 attached with a transparent electrode and fluorescent substance has been mounted. Accordingly, the structure is simple, production yield can be enhanced, and manufacturing of a large area is possible. Since this uses the carbon nanotube 34 oriented in the vertical direction as emitter tips, also, a large emission current can be obtained even with a low working voltage.