Single walled carbon nanotubes can be synthesized and production efficiency of carbon nanotubes can be enhanced by a method including a supplying step (S11) in which particulate carriers are supplied into a drum, a sputtering step (S12) for supporting a catalyst, in which sputtering is performed while this drum 10 is rotated around the axis and is swung so that one end portion and the other end portion in the axial direction of the drum 10 are relatively vertically switched, and a recovering step (S13) in which the particulate carriers are recovered by inclining the drum to discharge the particulate carriers from the drum.