The present invention is used to produce long carbon nanotubes used, for example, in automobile and/or aircraft industry. An object of the invention is to obtain bundles of multi-walled and well oriented nanotubes of sufficient length and provide stability of continuous nanotubes producing process. The method comprises introducing a carbon-bearing component, a promoter and a precursor of a carbon nanotube growth catalyst in a carrier gas stream to form a mixture of these components; passing said mixture through the a reactor heated to an operating temperature of 1000° C. to 1200° C. and removing nanotubes formed in the reactor into a product receiver. The mixture is fed in the reactor from the bottom upwards at a linear flow velocity of 50 mm/c to 130 mm/c. When the temperature in the reactor reaches said operating temperature, the linear flow velocity of the mixture is decreased to 4-10 mm/c, and the linear flow velocity is increased to 30-130 mm/c at the outlet of the reactor. The apparatus comprises means for introducing the carbon-bearing component, the promoter and the precursor of the carbon nanotube growth catalyst in the carrier gas stream, a vertical reactor with a working chamber, means for heating the working chamber to the operating temperature, means for delivering the mixture to the working chamber of the reactor and means for removing products from the working chamber. The chamber is made of three successive sections, namely a lower inlet 16 section, a middle 17 section and an upper outlet 18 section and the diameter of the lower section 16 is ⅕ to ⅓ of the diameter of the middle section 17, while the diameter of the upper section 18 is from ¼ to ⅓ of the diameter of the middle section 17.