Carbon nanotubes are more efficiently produced with a simpler apparatus. The process, which is for producing carbon nanotubes by the combustion method, is characterized by comprising: a step in which a catalyst-supporting powder comprising a base powder and a catalyst supported on the surface thereof is prepared; a step in which the catalyst-supporting powder is deposited on a porous support (2) having through-holes through which a flame passes, so that the powder particles are held in the through-holes without tenaciously adhering to one another; a step in which the porous support (2) having the catalyst-supporting powder held thereon is disposed in a combustion oven (1) in which one end (1b) is open; and a step in which a carbon-containing flame is generated in a burner part (3) disposed at the other end (1a) of the combustion oven (1) and the flame is fed to the through-holes of the porous support (2) to produce carbon nanotubes on the surface of the catalyst-supporting powder present in the through-holes.