In the growth of carbon nanotubes, the aggregation of catalytic fine particles therefor is a problem. In order to realize the growth of carbon nanotubes into a high density, the carbon nanotube growing process includes a first plasma treatment step of treating a surface having catalytic fine particles with a plasma species generated from a gas which contains at least hydrogen or a rare gas without carbon element, a second plasma treatment step of forming a carbon layer on the surface of the catalytic fine particles by a plasma generated from a gas which contains at least a hydrocarbon after the first plasma treatment step, and a carbon nanotube growing step of growing carbon nanotubes by use of a plasma generated from a gas which contains at least a hydrocarbon after the second plasma treatment step.